CN112964555A - Test and calculation method for measuring equivalent plastic strain forming limit diagram - Google Patents

Test and calculation method for measuring equivalent plastic strain forming limit diagram Download PDF

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CN112964555A
CN112964555A CN202110185037.6A CN202110185037A CN112964555A CN 112964555 A CN112964555 A CN 112964555A CN 202110185037 A CN202110185037 A CN 202110185037A CN 112964555 A CN112964555 A CN 112964555A
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肖锋
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Abstract

The invention discloses a test and calculation method for measuring an equivalent plastic strain forming limit diagram, which comprises the following steps: measuring the hole expansion rate or the uniform elongation rate of the material; calculating the real fracture strain or the real uniform strain of the belt edge damage; calculating real main strain and real secondary strain under different simple strain paths; and drawing an equivalent plastic strain forming limit curve. The method avoids various defects in the prior art, provides a feasible engineering solution for predicting the edge cracking of the advanced high-strength steel, reduces the material testing cost, and saves the labor cost and the equipment investment. The equivalent plastic strain forming limit curve determined by the method can be directly input into the existing forming simulation commercial software, the accuracy of a prediction result can be visually verified, and engineering application is accelerated, so that the method has important theoretical and engineering practical significance.

Description

Test and calculation method for measuring equivalent plastic strain forming limit diagram
Technical Field
The invention relates to a test and calculation method for measuring an equivalent plastic strain forming limit diagram, in particular to a test and calculation method for equivalent plastic strain, bilinear and single linear forming limit diagrams of uniform forming or belt edge damage.
Background
The shaping Limit Diagram (FLD) was proposed in the last 60 th century by Keeler (SAE technical paper 650535) and Goodwin (SAE technical paper 680093). Keeler has proposed that the right half regional analysis that is used for the sheet material to receive the simple strain state region of two tensile deformations, and Goodwin has expanded the analysis that the left half regional simple strain state region that is used for the sheet material to be drawn-pressure deformation on Keeler's basis.
FLD describes the extreme combination of true primary strain (ordinate) and true secondary strain (abscissa) near the local necked state at different simple strain paths covering from a purely uniaxial to a purely biaxial stretched state, the corresponding simple strain path β having a value in the range of [ -0.5,1], β being related to the value of r, i.e. the plastic strain ratio, as follows:
Figure BDA0002942759660000011
thus, one can translate into characterizing a simple strain path with the value of r.
Currently, forming limit diagrams have been considered by the industry as effective tools for evaluating sheet formability, and form mature industry standards, such as GB-T/15825.8-2008 (guide for determination of sheet metal forming performance and test method part 8: Forming Limit Diagram (FLD)), which sets up detailed test methods and procedures for how to determine the FLD of a sheet. In brief, firstly, test samples under several simple strain paths are manufactured and tested; secondly, after the test is finished, selecting and measuring the main strain and the secondary strain of the critical grid circle, and marking a measuring point in a forming limit diagram; and finally, fitting according to the distribution state of the measurement points to obtain a Forming Limit Curve (FLC) of the plate, wherein the Forming Limit Curve is generally V-shaped and is simply referred to as V-FLD or V-FLC.
In a standard forming limit diagram, the selection of a critical grid circle for measuring the main strain and the secondary strain is a judgment standard according to whether the critical state is in a local necking state, and the specific processing method in engineering is as follows: the mesh circle located in the neck region but not broken is taken as a critical mesh circle, or the mesh circle next to the neck or crack is taken as a critical mesh circle, or the mesh circle adjacent to the mesh circle where the neck or crack traverses its middle is taken as a critical mesh circle, and therefore, V-FLD cannot be used as a criterion for judging material failure in press analysis.
However, in the standard Forming Limit diagram, if the critical grid circle for measuring the main strain and the secondary strain is selected according to whether the critical grid circle is in the critical state of Fracture, the Fracture Forming Limit (FFL for short) of the sheet is obtained by fitting, and if the value range of the simple strain path β is [0,1], according to the volume invariant condition:
ε1+ε2+ε3＝0 (2)
in the critical state of fracture, the strain in the thickness direction is approximately equal to a constant ε3About const, then equation (1) may be changed to:
ε1＝-ε2+const. (3)
thus, in the forming limit diagram, FFL approximates a straight line with a slope of "-1".
The FLD provides a technical basis and a practical criterion for conveniently researching the plate forming limit, evaluating the plate forming performance and solving a plurality of problems in the plate forming field, so the FLD is integrated into commercial stamping simulation software and is used for judging the plate forming risk.
However, with the large number of applications of Advanced High Strength Steels (AHSS), conventional FLDs have repeatedly proven to be unusable for predicting AHSS edge cracking, such as:
view of the united states steel company (USS): "The applicability of The adaptive of The conditional limiting dimension splitting in high-band structure grades of AHSS is not associated with restricted partitioning, up high The conditional limiting dimension is defined [1,3]. The applicability of The conventional forming limit diagram is challenged because cracking in advanced high-strength steels is generally not associated with a local neck, whereas The conventional forming limit diagram is defined on this basis (SAE 2007-01-1693); the edge fracture limit of AHSS is lower than that of conventional steel Due to high strength and multi-phase structure and cannot be predicted by conventional Forming Limit Curve (FLC) (SAE 2014-01-0985). "
General automotive view (GDIS 2010): "structural FEA soft to prediction edge fragment based on FLC; the conventional finite element analysis method cannot predict edge cracking, and the finite element analysis program and failure criterion are to be improved. "
Ford automotive view (SAE 2015-01-0525): "the FLD or SFLD can not be used to predict the edge failure because the edge strain is often lower than that of the traditional FLD or SFLD. "
View of the public automobile (IDDRG 2016): up to now, it has not been possible to predict the formation of such cracks (edge cracks) accurately by using the existing experimental and simulation methods. "
View of Honda automobile (SAE 2017-01-0308): "Edge cracking in the stamping production increases the rejection rate, which is difficult to predict using conventional stamping simulation techniques. "
Also, conventional FLDs cannot be used to predict AHSS local cracking, such as:
viewpoint of anseretatal (arcelormottal) (GDIS 2007): "Draw panel split, and restore panel cracked, in regions not predicted by FLD. Draw panel re-molded with FLD adjusted to sheet active failures, and process modified to insulation surface new local failure criterion Using FLD. "
General theory of labor in Massachusetts (MIT) (GDIS 2017): "Fractures on light rad two reducing stationary cylindrical by Forming Limit Diagram (FLD). The Forming Limit Diagram (FLD) does not predict fracture at small chamfers during stamping.
How is the edge cracking of Advanced High Strength Steel (AHSS) judged? Currently, there are three main evaluation indexes of edge cracking, namely, hole expansion rate, edge thinning rate and maximum principal strain, wherein the hole expansion rate is more and more approved, for example, from the perspective of USS (SAE 2007-01-1693): "The hole expansion ratio obtained by The taper hole expansion test can be used as The limit of stretch flanging, which can be used as The failure criterion for evaluating edge crack by computer simulation. "; ottoman (Voestalpine) opinion (Edge crack Simulation with the modular "smiley" forming tool, 2016): "the evaluation of the treatment after edge failure is improved to some extent by using the tapered ISO16630 hole expansion statistical method compared with the FLC method only" in the present invention, the evaluation of the treatment after edge failure is improved to some extent by using the tapered ISO16630 hole expansion statistical method.
In the Advanced High Strength Steel (AHSS) edge cracking problem, the hole expansion ratio is widely regarded because the part edge strain state and the hole expansion edge strain state have similarities, as set forth by the american steel company (USS) (SAE 2007-01-1693): "the average failure strain (main strain) along the edge in the hole expansion test can be calculated from the change in circumferential length between the original length and the final length at the time of the edge crack through the thickness, which is practically equal to the hole expansion ratio".
Under the reaming is experimental, the edge in hole satisfies simultaneously that the unipolar stretching state, all keep uniform deformation, axisymmetric, then has:
Figure BDA0002942759660000041
the above equation indicates that the hole expansion ratio is actually the engineering fracture strain at the hole edge, and the true fracture strain at the hole edge
Figure BDA0002942759660000042
It can be expressed in terms of reaming ratio:
Figure BDA0002942759660000043
in the literature, the calculation method of the true Fracture strain of the hole Edge has been agreed by experts and scholars in units such as Nippon Steel, Nitta J, Yoshida T, Development of the Practical Evaluation Test and a Study of Numerical Evaluations of Edge fragments for Stretch fluoride of Sheet Metal Forming, 2008), Australian Oldham (Voestalepine, 2016), United states Steel company (USS, 2017), gliding iron University of Waterloo, 2017, Anselitar (Archimer, 2018).
If the edge damage generated by the punching process of the reaming test sample is consistent with the edge damage generated by the trimming process of the part, the true fracture strain of the hole edge can be directly used for predicting the edge cracking of the part, such as from the viewpoint of the United states Steel company (USS) (SAE 2007-01-1693): "The hole expansion ratio is about 24.5% for this DP600 steel under a work case cutting condition". However, The maximum principal strain at The free edge is 26%, The minimum principal strain at The stretch hinge limit. this samples with The use of The stretch hinge margin and press compression in this case, The hole expansion ratio of DP600 steel is about 24.5% under The most unfavorable shearing conditions (similar to The die cutting conditions). However, the maximum primary strain of the free edge is 26%, exceeding the stretch-flanging limit. This means that in this case edge cracking can be predicted using the stretch flanging limit; this limit can be used to evaluate edge cracking under similar edge conditions or similar shear conditions. "
The inventor of the application submits 'patent application 2020106180963' of 'a test and calculation method for determining equivalent plastic strain forming limit diagram of material' in 2020, in the application, a mathematical expression of real main strain and real secondary strain is derived mathematically, an equivalent plastic strain forming limit diagram (EPS-FLD) of the material is drawn, and in the undamaged EPS-FLD, a damage coefficient is introduced through a hole expansion rate to correct the undamaged EPS-FLD so as to achieve the purpose of predicting edge cracking, so that the edge cracking and local cracking are unified into one evaluation standard, and meanwhile, the traditional complicated test measurement is avoided. The theoretical basis for predicting edge cracking in this application is: edge damage does not affect the true fracture strain of the material but affects the strain path at the edge, whereas the true fracture strain at the edge of the hole is the inflection point of the uniaxial strain path.
In the process of continuous research, the inventor of the application finds that the traditional V-FLD criterion has technical defects on a test method and the defects of the patent application 2020106180963 on engineering application:
firstly, the deformation degree of the critical grid circle is judged according to the main strain and the secondary strain measured under different simple strain paths, and it is difficult to ensure the same deformation level, and the V-FLC curve does not conform to the theoretical prediction result in form-the FLC curve is a standard ellipse (MIT, one fractional circulation in the equivalent strain and stress triaxiality space, 2004). According to the condition of unchanged volume, the real main strain and the real secondary strain are measured under the mesh circle with the diameter of 2.5mm, the real strain in the thickness direction is also given mathematically, and under the condition of large deformation, the real strain in the thickness direction is not equal to the real strain in the physical meaning thickness direction, because the mesh circle with the diameter of 2.5mm cannot ensure uniform deformation in the thickness direction, generally speaking, the uniform deformation in the thickness direction can be ensured only when the diameter of the mesh circle is equal to 1.0 mm. Meanwhile, the conventional V-FLC needs to be obtained through complicated experiments, and the experimental results are influenced by many factors, such as a test tool, the material thickness of a sample, the n value, and the like.
Secondly, for the prediction result of the uniaxial stretching or nearly uniaxial stretching strain state area, the V-FLD does not contain shearing edge information, and is excessively biased to safety judgment, namely cannot be used for predicting edge cracking; for the prediction result of the biaxial stretching or near biaxial stretching strain state area, the V-FLD is also biased to safe judgment, namely the local cracking in the biaxial stretching state cannot be predicted; for the prediction result of the plane strain or the area close to the plane strain state, the V-FLD is biased to be conservative, namely the cracking risk is predicted and the cracking is not actually caused; for the shear strain state region, the V-FLD does not contain shear information and does not cover the region, so that no judgment can be made according to the V-FLD.
Thirdly, for the edge crack prediction of advanced high-strength steel (AHSS), 'patent application 2020106180963', the EPS-FLD corrected based on the hole expansion ratio brings obstacles to the engineering application of the application, and on one hand, the corrected EPS-FLD needs to be developed and integrated into the forming analysis software for the second time; on the other hand, the need to consider the node separation of the units involves modification of the kernel program of the profiling analysis software, and therefore it is not practical to implement engineering applications in a short time.
Fourth, for the range of the plastic strain ratio r, the range of r in "patent application 2020106180963" has only two cases: firstly, the value range of r of the main claim is [ - ∞, + ∞ ], and in the existing commercial forming software, the EPS-FLD in the value range cannot be input, so that the current engineering cannot be practically applied; secondly, the value range of r of the slave claims is [ -0.5,1], and the strain path of the shearing area is not covered in accordance with the existing V-FLD, so that the shearing deformation can not be predicted by the EPS-FLD of the slave claims.
Therefore, the V-FLD is questioned and is continuously improved and developed due to various defects in the prior art in the testing method and engineering application, and the invention is a breakthrough to the V-FLD and is a supplement and improvement to the patent application 2020106180963.
Disclosure of Invention
1. Technical problem to be solved by the invention
Aiming at the defects in the prior art, the technical problems to be solved by the invention are as follows: the hole expansion rate lambda of the material is determined through a hole expansion test, and then the true fracture strain with edge damage is obtained
Figure BDA0002942759660000061
Then, the equivalent plastic strain is theoretically calculated to be equal to
Figure BDA0002942759660000062
True principal strain epsilon under arbitrary simple strain path of timemajorAnd true secondary strain εmin orFurther drawing an equivalent plastic strain forming limit diagram with edge damage, and replacing the hole expanding rate lambda with the uniform elongation rate
Figure BDA0002942759660000063
Therefore, the equivalent plastic strain forming limit diagram under different conditions can be drawn on the basis of the measured material hole expansion rate and the uniform elongation rate and through theoretical calculation, and the defects in the prior art are directly avoided.
2. Technical scheme of the invention
In order to achieve the object of the technical problem to be solved by the present invention, the present invention provides a test and calculation method for determining an equivalent plastic strain forming limit diagram, comprising the steps of:
step one, measuring the hole expansion rate lambda of a material, wherein the hole expansion rate lambda is measured according to a test method specified by a hole expansion test standard;
step two, calculating the real fracture strain of the belt edge damage
Figure BDA0002942759660000064
True strain at break of said belt edge damage
Figure BDA0002942759660000065
Calculated as follows:
Figure BDA0002942759660000066
step three, respectively calculating the real principal strain epsilon under different simple strain paths according to the following two formulasmajorAnd true secondary strain εmin or：
Figure BDA0002942759660000067
Figure BDA0002942759660000068
Wherein r is the plastic strain ratio, used to characterize a simple strain path;
step four, using the real principal strain epsilonmajorAs ordinate, true secondary strain εmin orFor the abscissa, a coordinate system M is constructed, and the forming limit plotted according to the equations (1-2) and (1-3) is referred to as an equivalent plastic strain forming limit diagram with edge damage.
Furthermore, the plastic strain ratio r is taken to be in the range of [ -0.5,1]Then, corresponding emin orThe value range is [ -0.5. ln (1+ lambda.), 0.5. ln (1+ lambda) ]]Wherein the measured range of the distribution of the hole expansion ratio λ is (0, λ)max]Wherein λ ismaxRefers to the theoretical ultimate hole expansion rate of the material.
Further, in the fourth step, a plurality of r values are taken in turn and discontinuously, and the real principal strain epsilon corresponding to each r value is respectively calculated according to the formulas (1-2) and (1-3)majorAnd true secondary strain εmin orThe strain state [ epsilon ] corresponding to each r valuemin or,εmajor]The coordinate points are sequentially marked in the coordinate system M, and the coordinate points are sequentially connected to draw a forming limit, which is called a multi-linear forming limit diagram with edge damage.
Further, in step four, the strain state [ epsilon ] in the uniaxial tensile strain path is obtained according to the expressions (1-1), (1-2) and (1-3) by sequentially taking r values of three typical strain states and taking r as 1min or,εmajor]Is [ -0.5. ln (1+ lambda.), ln (1+ lambda) ]]It is marked as point O in the coordinate system M; taking r as 0, the strain state [ epsilon ] under the plane strain path is obtained according to the expressions (1-1), (1-2) and (1-3)min or,εmajor]Is composed of
Figure BDA0002942759660000071
It is marked as point P in the coordinate system M; taking r as-0.5, the strain state [ epsilon ] under the biaxial stretching strain path is obtained according to the formulas (1-1), (1-2) and (1-3)min or,εmajor]Is [ 0.5. ln (1+ lambda) ], 0.5. ln (1+ lambda) ]]It is marked as point Q in the coordinate system M; connecting O, P, Q three points in sequence to obtain two line segments OP and PQ, wherein the mathematical equations are as follows:
Figure BDA0002942759660000072
Figure BDA0002942759660000073
the forming limits plotted from the two line segments OP and PQ are referred to as a bilinear forming limit diagram with edge damage.
Further, in step four, the strain state [ epsilon ] in the uniaxial tensile strain path is obtained according to the expressions (1-1), (1-2) and (1-3) by taking the r values of two typical strain states in sequence and taking r as 1min or，εmajor]Is [ -0.5. ln (1+ lambda.), ln (1+ lambda) ]]It is marked as point O in the coordinate system M; taking r as-0.5, the strain state [ epsilon ] under the biaxial stretching strain path is obtained according to the formulas (1-1), (1-2) and (1-3)min or,εmajor]Is [ 0.5. ln (1+ lambda) ], 0.5. ln (1+ lambda) ]]It is marked as point Q in the coordinate system M; and connecting the points O and Q to obtain a line segment OQ, wherein the mathematical equation of the line segment OQ is as follows:
Figure BDA0002942759660000074
the forming limit plotted according to the line segment OQ is referred to as a single linear forming limit diagram with edge damage.
A test and calculation method for determining an equivalent plastic strain forming limit diagram comprises the following steps:
step one, measuring the uniform elongation of the material
Figure BDA0002942759660000075
Said uniform elongation
Figure BDA0002942759660000076
The method comprises the following steps: in the uniaxial tensile test, the length, width and height are taken to be l in the central region of the specimen fracturer·wr·h0The maximum engineering strain of the finite body A under uniform necking deformation is always calculated by the following formula:
Figure BDA0002942759660000077
wherein lrIs an initial gauge length, wrFor the initial width, the subscript r indicates the initial gauge length and the size of the initial width, h0Is the thickness of the sample,. alpha.UELMeans the measured deformation length of the finite body A at the end of uniform necking;
step two, calculating the real uniform strain
Figure BDA0002942759660000081
Said true uniform strain
Figure BDA0002942759660000082
Calculated as follows:
Figure BDA0002942759660000083
step three, dividing the mixture into the following two formulasRespectively calculating the true principal strain epsilon under different simple strain pathsmajorAnd true secondary strain εmin or：
Figure BDA0002942759660000084
Figure BDA0002942759660000085
Wherein r is the plastic strain ratio, used to characterize a simple strain path;
step four, using the real principal strain epsilonmajorAs ordinate, true secondary strain εmin orFor the abscissa, a coordinate system M is constructed, and the forming limit plotted according to the equations (2-3) and (2-4) is referred to as an equivalent plastic strain forming limit diagram of uniform deformation.
Furthermore, the plastic strain ratio r is taken to be in the range of [ -0.5,1]Then, corresponding emin orA value range of
Figure BDA00029427596600000810
Wherein the measured uniform elongation
Figure BDA00029427596600000811
In a distribution range of
Figure BDA00029427596600000812
Wherein the content of the first and second substances,
Figure BDA00029427596600000813
is the engineering strain at break of the material.
Further, in the fourth step, a plurality of r values are taken in turn and discontinuously, and the real principal strain epsilon corresponding to each r value is respectively calculated according to the formulas (2-3) and (2-4)majorAnd true secondary strain εmin orThe strain state [ epsilon ] corresponding to each r valuemin or,εmajor]The coordinate points are marked in the coordinate system M in sequence, the coordinate points are connected in sequence, and the drawn forming limit is called asA multi-linear shaping limit diagram for uniform shaping.
Further, in step four, the strain state [ epsilon ] in the uniaxial tensile strain path is obtained according to the expressions (2-2), (2-3) and (2-4) by sequentially taking r values of three typical strain states and taking r as 1min or,εmajor]Is composed of
Figure BDA00029427596600000814
It is marked as point O in the coordinate system M; taking r as 0, the strain state [ epsilon ] under the plane strain path is obtained according to the formulas (2-2), (2-3) and (2-4)min or,εmajor]Is composed of
Figure BDA0002942759660000086
It is marked as point P in the coordinate system M; taking r as-0.5, the strain state [ epsilon ] under the biaxial stretching strain path is obtained according to the formulas (2-2), (2-3) and (2-4)min or,εmajor]Is composed of
Figure BDA0002942759660000087
It is marked as point Q in the coordinate system M; connecting O, P, Q three points in sequence to obtain two line segments OP and PQ, wherein the mathematical equations are as follows:
Figure BDA0002942759660000088
Figure BDA0002942759660000089
the shaping limit plotted from the two line segments OP and PQ is referred to as a uniformly shaped bilinear shaping limit map.
Further, in step four, the strain state [ epsilon ] in the uniaxial tensile strain path is obtained according to the expressions (2-2), (2-3) and (2-4) by taking the r values of two typical strain states in sequence and taking r as 1min or,εmajor]Is composed of
Figure BDA0002942759660000091
In a coordinate system MMark it as point O; taking r as-0.5, the strain state [ epsilon ] under the biaxial stretching strain path is obtained according to the formulas (2-2), (2-3) and (2-4)min or,εmajor]Is composed of
Figure BDA0002942759660000092
It is marked as point Q in the coordinate system M; connecting the points O and Q to obtain a line segment OQ, wherein the mathematical equation is as follows:
Figure BDA0002942759660000093
the forming limit plotted according to the line segment OQ is referred to as a single linear forming limit diagram of uniform forming.
3. The invention has the advantages of
The invention provides a test and calculation method for measuring an equivalent plastic strain forming limit diagram, which avoids the defects of the prior art, and compared with the prior technical scheme, the test and calculation method has the following beneficial effects:
first, theoretical drawbacks are avoided. According to the traditional V-FLD, the yield surface of the three-dimensional strain space is concave, and according to the ' stay-on-the-go ' public design ', the yield surface of the three-dimensional strain space is convex in theory, the EPS-FLD strictly meets the outward convex characteristic of the yield surface, and the physical significance of the EPS-FLD is as follows: the strain states of all points on the curve are different, but equivalent plastic strains corresponding to all points are equal, meanwhile, V-FLD is not strict on the determination method, namely the determination of real main strain and real secondary strain is not verified by a volume invariant condition, and EPS-FLD is a theoretical calculation result strictly meeting the volume invariant condition.
Secondly, the practical engineering problem is solved. The traditional V-FLD is not measured at the edge of a sample, but is measured in the middle of the sample, the influence of a shearing edge process is not reflected, and the V-FLD cannot be used as the basis of edge cracking. Compared with the EPS-FLD provided by the invention, the EPS-FLD evaluation result is slightly conservative and is closer to the reality in uniaxial and biaxial strain states; in a plane strain state, the V-FLD evaluation result is slightly conservative; the EPS-FLD can be covered to a shear strain state. Therefore, the invention is based on theoretical innovation, so that the EPS-FLD can move along with the change of the hole expanding rate and the uniform elongation, the change of the structure, the material and the process can be reflected at the same time, the effective prediction of various failure modes generated in the stamping forming is realized by adopting the same technical standard, and thus, various defects in the traditional and static V-FLD are avoided, and a more effective technical solution is provided for the engineering problems encountered in the application of the automobile steel.
And thirdly, the material testing cost is reduced. Because the traditional V-FLD needs to make measurement samples under different simple strain paths and adopts special test equipment for measurement, and the V-FLD is related to the thickness of a test piece, so that the test work is greatly increased, time and labor are greatly consumed for measuring the traditional V-FLD, meanwhile, in order to solve the problem of edge cracking, a new evaluation standard is added to cause the addition of a new test method, and the test cost is further increased.
Fourthly, the engineering application is accelerated. Compared with the EPS-FLD modified in the patent application 2020106180963, the forming limit diagram of the invention is not required to be secondarily developed and integrated into the existing forming analysis software, and the kernel program of the existing forming analysis software is not required to be modified, and the forming limit diagram can be directly input into the commercial software like the traditional V-FLC data and used for the failure risk evaluation standard of the simulation result. In fact, according to the needs of engineering problems, through flexible value of the plastic strain ratio r, the proper EPS-FLD is determined, the invention recommends the range of r of EPS-FLD which can be used for the current commercial software to be [ -0.5, + ∞ ], and four types of simple strain paths of shearing, uniaxial stretching, plane strain and biaxial stretching are covered, therefore, the invention can be directly used for the engineering analysis of the stamping forming simulation of the current commercial software, and is favorable for promoting engineering application.
In conclusion, various problems exist in practical engineering application due to the defects of the traditional V-FLD in theory and method, and the technical requirement of light weight of the automobile steel under the new situation cannot be met. Through the implementation of the invention, the new material card formed by stamping the parts can be obtained at low cost, so the invention has important theoretical and engineering practical significance and brings very wide engineering application prospect.
Drawings
The present invention will be described in further detail with reference to the accompanying drawings.
FIG. 1 is a graph of the equivalent plastic strain forming limit of band edge damage at a 23% reaming ratio of example DP780 of the present invention;
FIG. 2 is a graph of the ideal equivalent plastic strain forming limit for example DP780 of the present invention;
FIG. 3 is three simple strain state point markers for band edge damage with a 23% reaming ratio of DP780 of an embodiment of the present invention;
FIG. 4 is a graph of the dual linear forming limit of band edge damage for example DP780 with a 23% hole expansion ratio of the present invention;
FIG. 5 is two simple strain state point markers for band edge damage with a hole expansion ratio of 23% for example DP780 of the present invention;
FIG. 6 is a single linear forming limit plot for band edge damage with a 23% reaming ratio for example DP780 of the present invention;
FIG. 7 is a graph of equivalent plastic strain forming limits for uniform formation of example DP780 of the present invention at gauge length 10 mm;
FIG. 8 is three simple strain state point markers for uniform elongation of 27.1% uniform deformation for example DP780 of the present invention;
FIG. 9 is a dual linear forming limit diagram for uniform deformation with a uniform elongation of 27.1% for example DP780 of the present invention;
FIG. 10 is two simple strain state point markers for uniform elongation of 27.1% uniform deformation for example DP780 of the present invention;
FIG. 11 is a single linear forming limit plot for example DP780 of the present invention with a uniform elongation of 27.1% uniform deformation;
FIG. 12 is a graph comparing the forming limit of band edge damage for example DP780 with a hole expansion ratio of 23% in accordance with the present invention;
FIG. 13 is a uniform forming limit contrast plot for example DP780 of the present invention with a uniform elongation of 27.1%.
Detailed Description
The technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings.
Example 1
In this example, the testing and calculating method for determining the equivalent plastic strain forming limit diagram according to the present invention is described in detail with reference to the material DP780/1.4mm, and comprises the following steps:
step one, according to a test method specified by a material reaming test standard ISO/TS 16630 or GB/T2424242454-;
step two, calculating the real fracture strain of the belt edge damage
Figure BDA0002942759660000111
True strain at break of said belt edge damage
Figure BDA0002942759660000112
Calculated as follows:
Figure BDA0002942759660000113
step three, respectively calculating the real principal strain epsilon under different simple strain paths according to the following two formulasmajorAnd true secondary strain εmin or：
Figure BDA0002942759660000114
Figure BDA0002942759660000115
Wherein r is a plastic strain ratio and is used for representing a simple strain path, and the value range of r is [ -0.5,1]Then, corresponding emin orThe value range is [ -0.104,0.104 [)]According to (1-1), (1-2) andthe real primary strain and the real secondary strain in different simple strain states obtained by the calculation of the formula (1-3) are shown in table 1.
Table 1 example 1 true principal and true secondary strains at different simple strain states
Figure BDA0002942759660000116
Step four, using the real principal strain epsilonmajorAs ordinate, true secondary strain εmin orA coordinate system M is constructed for the abscissa, and the forming limit plotted by using the data in Table 1 is called an equivalent plastic strain forming limit diagram with edge damage, and the equivalent plastic strain forming limit diagram with DP780 hole expanding rate of 23% with edge damage shown in FIG. 1 is marked as EPS-FLC&HER 23% for predicting edge cracking phenomenon in part stamping simulation.
If the hole expansion rate lambda of DP780 is equal to the theoretical limit hole expansion rate lambdamaxSaid theoretical ultimate rate of expansion λmaxCalculated as follows:
Figure BDA0002942759660000121
wherein the content of the first and second substances,
Figure BDA0002942759660000122
is the true strain at break of the material, according to the method described in "a test and calculation method for determining the true stress-strain curve of the material, application No. 2019108010771", that is, in the uniaxial tension test, in the local necking deformation stage, in the sample fracture center region, the length and width are taken to be 1.0 mm.1.0 mm.h0Is always at the maximum true strain under uniform neck-down deformation,
Figure BDA0002942759660000123
calculated using the formula:
Figure BDA0002942759660000124
wherein lfIs the deformation length h of the finite body B at the moment of fracture0The true strain at break of DP780 was determined for the specimen thickness
Figure BDA0002942759660000125
The engineering strain corresponding to the true fracture strain of the gauge length of 1.0mm is equal to 53.7 percent, the drawn forming limit is called as an equivalent plastic strain forming limit graph without edge damage or ideal, the DP780 ideal equivalent plastic strain forming limit graph shown in figure 2 is marked as EPS-FLC&UEL53.7％_1.0mm。
In step four, if the r values of the three typical strain states are taken in sequence, and r is 1, the strain state [ epsilon ] in the uniaxial tensile strain path is obtained according to the expressions (1-1), (1-2) and (1-3)min or,εmajor]Is [ -0.104,0.207 ]]It is marked as point O in the coordinate system M; taking r as 0, the strain state [ epsilon ] under the plane strain path is obtained according to the expressions (1-1), (1-2) and (1-3)min or,εmajor]Is [0,0.179 ]]It is marked as point P in the coordinate system M; taking r as-0.5, the strain state [ epsilon ] under the biaxial stretching strain path is obtained according to the formulas (1-1), (1-2) and (1-3)min or,εmajor]Is [0.104,0.104 ]]Marking the strain point as a Q point in a coordinate system M, and marking three simple strain state points with edge damage, wherein the DP780 hole expansion rate is 23 percent as shown in figure 3; connecting O, P, Q three points in sequence to obtain two line segments OP and PQ, wherein the mathematical equations are as follows:
εmajor＝-0.268·εmin or+0.179，-0.104≤εmin or≤0 (1-4)
εmajor＝-0.732·εmin or+0.179，0≤εmin or≤0.104 (1-5)
the forming limit plotted according to the two line segments OP and PQ is called a double linear forming limit diagram with edge damage, and a double linear forming limit diagram with the DP780 hole expanding rate of 23% with edge damage shown in FIG. 4 is marked as Bilinear-FLC & HER 23% and is used for predicting the edge cracking phenomenon in the part stamping simulation.
In step four, if the r values of two typical strain states are taken in sequence, and r is 1, the strain state [ epsilon ] in the uniaxial tensile strain path is obtained according to the expressions (1-1), (1-2) and (1-3)min or,εmajor]Is [ -0.104,0.207 ]]It is marked as point O in the coordinate system M; taking r as-0.5, the strain state [ epsilon ] under the biaxial stretching strain path is obtained according to the formulas (1-1), (1-2) and (1-3)min or,εmajor]Is [0.104,0.104 ]]Marking the strain state point as a Q point in a coordinate system M, and marking two simple strain state points with edge damage, wherein the DP780 hole expansion rate is 23 percent as shown in FIG. 5; connecting O, Q the two points to obtain a line OQ, the mathematical equation of which is as follows:
Figure BDA0002942759660000131
the forming limit plotted according to the line OQ is called a single linear forming limit diagram with edge damage, and a single linear forming limit diagram with the DP780 hole expanding rate of 23% and the edge damage shown in FIG. 6 is marked as Unilinear-FLC & HER 23% and is used for predicting the edge cracking phenomenon in the part punching simulation.
Example 2
In this example, the testing and calculating method for determining the equivalent plastic strain forming limit diagram according to the present invention is described in detail with reference to the material DP780/1.4mm, and comprises the following steps:
step one, measuring the uniform elongation of the material
Figure BDA0002942759660000132
Said uniform elongation
Figure BDA0002942759660000133
The method comprises the following steps: in the uniaxial tensile test, the length, width and height are taken to be l in the central region of the specimen fracture10·w10Maximum engineering strain for a 1.4mm finite body a at uniform neck-in deformation at all times, calculated using the following formula:
Figure BDA0002942759660000134
wherein, the initial scale distance l1010mm, initial width wr10mm, the subscript r 10 indicating the size of the initial gauge length and initial width, lUELIt means that the deformation length of the finite body A at the end of uniform necking was measured to be 12.71 mm.
Step two, calculating the real uniform strain
Figure BDA0002942759660000135
Said true uniform strain
Figure BDA0002942759660000136
Calculated as follows:
Figure BDA0002942759660000137
step three, respectively calculating the real principal strain epsilon under different simple strain paths according to the following two formulasmajorAnd true secondary strain εmin or：
Figure BDA0002942759660000138
Figure BDA0002942759660000139
Wherein r is a plastic strain ratio and is used for representing a simple strain path, and the value range of r is [ -0.5,1](Note: in practical engineering applications, the R value range of EPS-FLD recommended to be used in current commercial software is [ -0.5, + ∞)]Fully predictive of four failure modes for shear, uniaxial, plane strain, and biaxial), then the corresponding epsilonmin orThe value range is [ -0.12,0.12 [)]The real primary strain and the real secondary strain in different simple strain states are calculated according to the expressions (2-2), (2-3) and (2-4), and are shown in table 2.
Table 2 example 2 true principal and true secondary strains under different simple strain conditions
Figure BDA0002942759660000141
Step four, using the real principal strain epsilonmajorAs ordinate, true secondary strain εmin orFor the construction of the coordinate system M on the abscissa, the forming limits plotted in Table 2 are referred to as the equivalent plastic strain forming limit diagram for uniform forming, and the equivalent plastic strain forming limit diagram for uniform forming with a gauge length of 10mm DP780 shown in FIG. 7 is referred to as EPS-FLC&UEL 27.1% _10mm, can be used to predict localized cracking in part stamping simulations.
If taking the uniform elongation of DP780
Figure BDA0002942759660000142
Equal to engineering strain at break of the material
Figure BDA0002942759660000143
Said engineering strain at break
Figure BDA0002942759660000144
The method comprises the following steps: in the uniaxial tensile test, the maximum engineering strain of the finite element B with the length, width and height of 1.0mm 1.4mm in the fracture center region of the sample under uniform necking deformation is always calculated by the following formula:
Figure BDA0002942759660000145
wherein the length of deformation l of the finite body B at the moment of fracturefThe drawn forming limit is called an ideal equivalent plastic strain forming limit graph, the ideal equivalent plastic strain forming limit graph of the DP780 with the gauge length of 1.0mm is shown in FIG. 2, and the graph is marked as EPS-FLC&UEL53.7％_1.0mm。
In step four, if the r values of the three typical strain states are taken in sequence, the r is taken to be 1The strain state [ epsilon ] in the uniaxial tensile strain path is obtained from the expressions (2-2), (2-3) and (2-4)min or,εmajor]Is [ -0.120,0.240 ]]It is marked as point O in the coordinate system M; taking r as 0, the strain state [ epsilon ] under the plane strain path is obtained according to the formulas (2-2), (2-3) and (2-4)min or,εmajor]Is [0,0.208 ]]It is marked as point P in the coordinate system M; taking r as-0.5, the strain state [ epsilon ] under the biaxial stretching strain path is obtained according to the formulas (2-2), (2-3) and (2-4)min or,εmajor]Is [0.120,0.120 ]]Labeled as point Q in the coordinate system M, three simple strain state points labeled as uniformly deformed with a DP780 uniform elongation of 27.1% as shown in fig. 8. Connecting O, P, Q three points in sequence to obtain two line segments OP and PQ, wherein the mathematical equations are as follows:
εmajor＝-0.268·εmin or+0.208，-0.120≤εmin or≤0 (2-5)
εmajor＝-0.732·εmin or+0.208，0≤εmin or≤0.120 (2-6)
the forming limit plotted according to the two line segments OP and PQ is called a uniform deformation double-linear forming limit diagram, and a DP780 uniform elongation 27.1% uniform deformation double-linear forming limit diagram shown in FIG. 9, and the curve is marked as Bilinear-FLC & UEL 27.1% _10mm, and can be used for predicting the local cracking phenomenon in the part stamping simulation.
In step four, if the r values of two typical strain states are taken in sequence, and r is taken to be 1, the strain state [ epsilon ] under the uniaxial tensile strain path is obtained according to the expressions (2-2), (2-3) and (2-4)min or,εmajor]Is [ -0.120,0.240 ]]It is marked as point O in the coordinate system M; taking r as-0.5, the strain state [ epsilon ] under the biaxial stretching strain path was obtained from the formulas ((2-2), (2-3) and (2-4)min or,εmajor]Is [0.120,0.120 ]]Marked as point Q in the coordinate system M, as shown in fig. 10 for two simple strain state point markers with a DP780 uniform elongation of 27.1% uniform deformation; connecting O, Q the two points to obtain a line OQ, the mathematical equation of which is as follows:
Figure BDA0002942759660000151
the forming limit plotted according to the line OQ is called a single linear forming limit diagram of uniform deformation, and a single linear forming limit diagram of DP780 uniform elongation of 27.1% uniform deformation shown in FIG. 11, and the curve is marked as Unilinear-FLC & UEL 27.1% _10mm, and can be used for predicting a local cracking phenomenon in part stamping simulation.
The forming limit curve of the band edge damage with the medium hole expansion rate of 23% of example 1 is plotted in one graph, the forming limit contrast graph of the band edge damage with the DP780 hole expansion rate of 23% shown in fig. 12, the uniaxial strain states of the forming limit curves of the three band edge damages of EPS-FLC & HER 23%, bifilar-FLC & HER 23%, Unilinear-FLC & HER 23% are completely coincident, and the three forming limit curves are used for predicting the edge cracking phenomenon in the part punching simulation and have the same prediction accuracy.
The uniform forming limit curve of 27.1% medium uniform elongation of example 2 is plotted in a graph, such as the uniform forming limit comparison graph of DP780 uniform elongation of 27.1% shown in FIG. 13, and the results of Unilinear-FLC & UEL 27.1% _10mm prediction are more conservative for predicting localized cracking in part stamping simulation, and EPS-FLC & UEL 27.1% _10mm and Biliner-FLC & UEL 27.1% _10mm can be considered to have the same prediction accuracy.
The above embodiments are only exemplary embodiments of the present invention, and are not intended to limit the present invention, and the scope of the present invention is defined by the claims. Various modifications and equivalents may be made by those skilled in the art within the scope of the invention as defined by the appended claims.

Claims (10)

1. A test and calculation method for determining an equivalent plastic strain forming limit diagram comprises the following steps:
step one, measuring the hole expansion rate lambda of a material, wherein the hole expansion rate lambda is measured according to a test method specified by a hole expansion test standard;
step two, calculating the belt edgeTrue strain at break of damage
Figure FDA0002942759650000011
True strain at break of said belt edge damage
Figure FDA0002942759650000012
Calculated as follows:
Figure FDA0002942759650000013
step three, respectively calculating the real principal strain epsilon under different simple strain paths according to the following two formulasmajorAnd true secondary strain εminor：
Figure FDA0002942759650000014
Figure FDA0002942759650000015
Wherein r is the plastic strain ratio, used to characterize a simple strain path;
step four, using the real principal strain epsilonmajorAs ordinate, true secondary strain εminorFor the abscissa, a coordinate system M is constructed, and the forming limit plotted according to the equations (1-2) and (1-3) is referred to as an equivalent plastic strain forming limit diagram with edge damage.
2. A test and calculation method for determining an equivalent plastic strain forming limit diagram according to claim 1, characterized in that: the plastic strain ratio r is taken to be in the range of [ -0.5,1 [)]Then, corresponding eminorThe value range is [ -0.5. ln (1+ lambda.), 0.5. ln (1+ lambda) ]]Wherein the measured range of the distribution of the hole expansion ratio λ is (0, λ)max]Wherein λ ismaxRefers to the theoretical ultimate hole expansion rate of the material.
3. A test and calculation method for determining an equivalent plastic strain forming limit diagram according to claim 1 or 2, characterized in that: in the fourth step, a plurality of r values are taken in turn and discontinuously, and the real principal strain epsilon corresponding to each r value is respectively calculated according to the formulas (1-2) and (1-3)majorAnd true secondary strain εminorThe strain state [ epsilon ] corresponding to each r valueminor,εmajor]The coordinate points are sequentially marked in the coordinate system M, and the coordinate points are sequentially connected to draw a forming limit, which is called a multi-linear forming limit diagram with edge damage.
4. A test and calculation method for determining an equivalent plastic strain forming limit diagram according to claim 3, characterized in that: in the fourth step, the strain state [ epsilon ] in the uniaxial tensile strain path is obtained according to the expressions (1-1), (1-2) and (1-3) by sequentially taking r values of three typical strain states and taking r as 1minor,εmajor]Is [ -0.5. ln (1+ lambda.), ln (1+ lambda) ]]It is marked as point O in the coordinate system M; taking r as 0, the strain state [ epsilon ] under the plane strain path is obtained according to the expressions (1-1), (1-2) and (1-3)minor,εmajor]Is composed of
Figure FDA0002942759650000016
It is marked as point P in the coordinate system M; taking r as-0.5, the strain state [ epsilon ] under the biaxial stretching strain path is obtained according to the formulas (1-1), (1-2) and (1-3)minor,εmajor]Is [ 0.5. ln (1+ lambda) ], 0.5. ln (1+ lambda) ]]It is marked as point Q in the coordinate system M; connecting O, P, Q three points in sequence to obtain two line segments OP and PQ, wherein the mathematical equations are as follows:
Figure FDA0002942759650000021
Figure FDA0002942759650000022
the forming limits plotted from the two line segments OP and PQ are referred to as a bilinear forming limit diagram with edge damage.
5. A test and calculation method for determining an equivalent plastic strain forming limit diagram according to claim 3, characterized in that: in step four, the values of r of two typical strain states are sequentially taken, r is taken as 1, and the strain state [ epsilon ] under the uniaxial tensile strain path is obtained according to the expressions (1-1), (1-2) and (1-3)minor,εmajor]Is [ -0.5. ln (1+ lambda.), ln (1+ lambda) ]]It is marked as point O in the coordinate system M; taking r as-0.5, the strain state [ epsilon ] under the biaxial stretching strain path is obtained according to the formulas (1-1), (1-2) and (1-3)minor,εmajor]Is [ 0.5. ln (1+ lambda) ], 0.5. ln (1+ lambda) ]]It is marked as point Q in the coordinate system M; and connecting the points O and Q to obtain a line segment OQ, wherein the mathematical equation of the line segment OQ is as follows:
Figure FDA0002942759650000023
the forming limit plotted according to the line segment OQ is referred to as a single linear forming limit diagram with edge damage.
6. A test and calculation method for determining an equivalent plastic strain forming limit diagram comprises the following steps:
step one, measuring the uniform elongation of the material
Figure FDA0002942759650000024
Said uniform elongation
Figure FDA0002942759650000025
The method comprises the following steps: in the uniaxial tensile test, the length, width and height are taken to be l in the central region of the specimen fracturer·wr·h0The maximum engineering strain of the finite body A under uniform necking deformation is always calculated by the following formula:
Figure FDA0002942759650000026
wherein lrIs an initial gauge length, wrFor the initial width, the subscript r indicates the initial gauge length and the size of the initial width, h0Is the thickness of the sample,. alpha.UELMeans the measured deformation length of the finite body A at the end of uniform necking;
step two, calculating the real uniform strain
Figure FDA0002942759650000027
Said true uniform strain
Figure FDA0002942759650000028
Calculated as follows:
Figure FDA0002942759650000029
step three, respectively calculating the real principal strain epsilon under different simple strain paths according to the following two formulasmajorAnd true secondary strain εminor：
Figure FDA00029427596500000210
Figure FDA0002942759650000031
Wherein r is the plastic strain ratio, used to characterize a simple strain path;
step four, using the real principal strain epsilonmajorAs ordinate, true secondary strain εminorFor the abscissa, a coordinate system M is constructed, and the forming limit plotted according to the equations (2-3) and (2-4) is referred to as an equivalent plastic strain forming limit diagram of uniform deformation.
7. A test and calculation method for determining an equivalent plastic strain forming limit diagram according to claim 6, characterized in that: the plastic strain ratio r is taken to be in the range of [ -0.5,1 [)]Then, corresponding eminorA value range of
Figure FDA0002942759650000032
Wherein the measured uniform elongation
Figure FDA0002942759650000033
In a distribution range of
Figure FDA0002942759650000034
Wherein the content of the first and second substances,
Figure FDA0002942759650000035
is the engineering strain at break of the material.
8. A test and calculation method for determining an equivalent plastic strain forming limit diagram according to claim 6 or 7, characterized in that: in the fourth step, a plurality of r values are taken in turn and discontinuously, and the real principal strain epsilon corresponding to each r value is respectively calculated according to the formulas (2-3) and (2-4)majorAnd true secondary strain εminorThe strain state [ epsilon ] corresponding to each r valueminor,εmajor]The coordinate points are sequentially marked in the coordinate system M, the coordinate points are sequentially connected, and the drawn forming limit is called a multi-linear forming limit diagram of uniform forming.
9. A test and calculation method for determining an equivalent plastic strain forming limit diagram according to claim 8, characterized in that: in the fourth step, the strain state [ epsilon ] of the uniaxial tensile strain path is obtained according to the expressions (2-2), (2-3) and (2-4) by sequentially taking the r values of three typical strain states and taking r as 1minor,εmajor]Is composed of
Figure FDA0002942759650000036
In the coordinateIt is marked as point O in line M; taking r as 0, the strain state [ epsilon ] under the plane strain path is obtained according to the formulas (2-2), (2-3) and (2-4)minor,εmajor]Is composed of
Figure FDA0002942759650000037
It is marked as point P in the coordinate system M; taking r as-0.5, the strain state [ epsilon ] under the biaxial stretching strain path is obtained according to the formulas (2-2), (2-3) and (2-4)minor，εmajor]Is composed of
Figure FDA0002942759650000038
It is marked as point Q in the coordinate system M; connecting O, P, Q three points in sequence to obtain two line segments OP and PQ, wherein the mathematical equations are as follows:
Figure FDA0002942759650000039
Figure FDA00029427596500000310
the shaping limit plotted from the two line segments OP and PQ is referred to as a uniformly shaped bilinear shaping limit map.
10. A test and calculation method for determining an equivalent plastic strain forming limit diagram according to claim 8, characterized in that: in step four, taking the r values of two typical strain states in sequence, taking r as 1, and obtaining the strain state [ epsilon ] under the uniaxial tensile strain path according to the expressions (2-2), (2-3) and (2-4)minor，εmajor]Is composed of
Figure FDA00029427596500000311
It is marked as point O in the coordinate system M; taking r as-0.5, the strain state [ epsilon ] under the biaxial stretching strain path is obtained according to the formulas (2-2), (2-3) and (2-4)minor,εmajor]Is composed of
Figure FDA0002942759650000041
It is marked as point Q in the coordinate system M; connecting the points O and Q to obtain a line segment OQ, wherein the mathematical equation is as follows:
Figure FDA0002942759650000042
the forming limit plotted according to the line segment OQ is referred to as a single linear forming limit diagram of uniform forming.
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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113587880A (en) * 2021-07-27 2021-11-02 肖锋 Test and calculation method for measuring hole expansion rate
CN114544383A (en) * 2021-12-23 2022-05-27 武汉上善仿真科技有限责任公司 Test method for measuring ultimate sharp cold bend angle and equivalent fracture strain

Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110501224A (en) * 2019-08-28 2019-11-26 肖锋 A kind of test and calculation method measuring material true stress―strain curve
CN111896373A (en) * 2020-06-30 2020-11-06 武汉上善仿真科技有限责任公司 Test and calculation method for measuring equivalent plastic strain forming limit diagram

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110501224A (en) * 2019-08-28 2019-11-26 肖锋 A kind of test and calculation method measuring material true stress―strain curve
CN111896373A (en) * 2020-06-30 2020-11-06 武汉上善仿真科技有限责任公司 Test and calculation method for measuring equivalent plastic strain forming limit diagram

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
BRANDON M. HANCE ET AL.: "The Influence of Edge Preparation Method on the Hole Expansion Performance of Automotive Sheet Steels", SAE TECHNICAL PAPER, pages 367 - 369 *

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113587880A (en) * 2021-07-27 2021-11-02 肖锋 Test and calculation method for measuring hole expansion rate
CN114544383A (en) * 2021-12-23 2022-05-27 武汉上善仿真科技有限责任公司 Test method for measuring ultimate sharp cold bend angle and equivalent fracture strain
CN114544383B (en) * 2021-12-23 2024-03-15 武汉上善仿真科技有限责任公司 Test method for measuring extreme tip cold bending angle and equivalent fracture strain

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