CN112989654A - Finite element method for predicting laser shock forming limit under shock load - Google Patents

Finite element method for predicting laser shock forming limit under shock load Download PDF

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CN112989654A
CN112989654A CN202110209956.2A CN202110209956A CN112989654A CN 112989654 A CN112989654 A CN 112989654A CN 202110209956 A CN202110209956 A CN 202110209956A CN 112989654 A CN112989654 A CN 112989654A
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杨海亮
王霄
张焘
李哲文
倪鹏
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Abstract

The invention provides a finite element method for predicting laser impact forming limit under impact load, which relates to a damage failure forming technology of a sheet metal component, and comprises the steps of firstly, establishing a finite element model of the damage failure of the sheet metal component under Gaussian distribution impact load; secondly, establishing a hardening elastic-plastic constitutive model; then, writing an ABAQUS user dynamic material subprogram module by using a FORTRAN language, and realizing the proposed elastoplasticity constitutive model by using a central difference algorithm; and finally, embedding a subprogram into ABAQUS, calculating the high strain rate forming process of the laser impact sheet metal member, and further predicting the mechanical behavior of the sheet metal member, wherein the forming limit of the sheet metal member is judged by utilizing a maximum strain rate criterion. The forming limit of the sheet metal component is predicted by utilizing the established finite element model, and the given forming limit diagram has good reference value for researching the forming property of the sheet metal component in laser dynamic high strain rate forming.

Description

Finite element method for predicting laser shock forming limit under shock load
Technical Field
The invention relates to the field of prediction of forming failure of a sheet metal component, in particular to a finite element method for predicting laser shock forming limit of the sheet metal component under shock load.
Background
Laser shock peening is a high strain rate machining technique that uses a pulsed laser to vaporize and ionize an ablative coating, thereby creating a complex three-dimensional structure, particularly suited for the machining of micro-formed structures. Meanwhile, laser shock forming is not limited by the size of the die as compared to conventional sheet forming techniques (such as stamping and deep drawing) because the expansion of the plasma generated by the laser pulses is responsible for applying pressure to the workpiece. Compared with other processing technologies (such as a photoetching technology), the laser shock forming has the advantages of low cost and high speed, and is suitable for forming different materials and various three-dimensional shapes. However, due to the lack of measurement techniques on the micro-scale and sub-micro-scale, the formability of workpieces in laser shock forming is rarely studied.
The accurate description of the constitutive relation of the material is a precondition for predicting the mechanical behavior of the metal material under the impact load. The constitutive relation of materials in the current research center adopts a Johnson-Cook model carried by ABAQUS finite element software, and the model reflects the strain influence and the strain rate influence of the materials. However, since laser shock forming is a high strain rate forming process technique, the strain rate sensitivity of the material increases at high strain rate forming.
Disclosure of Invention
In view of the above problems, the present invention provides a prediction technique for damage failure forming limit of a thin plate metal member, which aims to predict the strain rate sensitivity of the thin plate metal member in the laser shock high strain rate forming process.
The invention is realized by the following technical scheme:
a finite element method adapted for predicting laser shock forming limits, comprising the steps of:
step 1: establishing a finite element model of damage failure of the sheet metal component under the Gaussian distribution impact load;
step 2: establishing a material rate related hybrid hardening elastoplasticity constitutive model comprehensively considering strain hardening, strain rate strengthening and high strain rate sensitivity;
and step 3: the method comprises the following steps of writing ABAQUS/VUMAT by using FORTRAN language, namely an ABAQUS user dynamic material subprogram module, and realizing the proposed elastoplasticity constitutive model by using a central difference algorithm;
and 4, step 4: and embedding the subprogram into ABAQUS, calculating the high strain rate forming process of the laser impact sheet metal member, and further predicting the mechanical behavior of the metal material, wherein the forming limit of the metal material can be judged by utilizing a maximum strain rate criterion.
The step (1) is specifically as follows:
firstly, establishing a finite element model of a sheet metal component; secondly, setting the material property of the sheet metal component; then, setting analysis step time according to the pulse width of the laser, and applying Gaussian distribution impact load to the sheet metal component after the analysis step is set; and finally, dividing the grid and submitting the operation.
The step (2) is specifically as follows:
under the condition of high strain rate, the flow stress is underestimated by simulating laser dynamic forming by using a Johnson-cook constitutive model, the sensitivity of the material becomes quite large in a high strain rate range, therefore, in order to describe the behavior of the material more accurately, the Johnson-cook constitutive model is modified so as to be suitable for the working condition of laser dynamic high strain rate forming, and the modified model is as follows:
Figure BDA0002951932350000021
wherein A is the yield strength under quasi-static state; b is a strain strengthening coefficient; ε is the plastic strain; epsilon0Is a reference strain; n is the strain hardening coefficient; c is a strain rate strengthening coefficient;
Figure BDA0002951932350000022
is the critical strain rate;
Figure BDA0002951932350000023
is a reference strain rate;
Figure BDA0002951932350000024
is the strain rate; m is the strain rate sensitivity coefficient, Ln is the pairAnd (4) counting.
The step (3) is specifically as follows:
step (3.1) establishing an elastoplasticity mechanical relationship of the metal material:
defined by the material model, the strain rate and total strain can be decomposed into an elastic part and a plastic part:
dε＝dεel+dεpl
ε＝εel+εpl
wherein epsilonelIs an elastic strain; epsilonplRepresenting plastic strain.
According to the radial return method, it is first assumed that the material elements are still in the elastic phase, and the strains that occur are all elastic strains, i.e. Δ ∈ ═ Δ ∈e. The elastic deformation is assumed to be linearly isotropic, and the relationship between the bulk modulus λ and the shear modulus G and young's modulus E is:
Figure BDA0002951932350000025
Figure BDA0002951932350000026
wherein ν is the poisson's ratio.
In general, the stress of a metal material can be decomposed into a spherical stress tensor (hydrostatic stress) σmSum bias stress tensor SijTwo parts. Wherein the global stress tensor induces the full elastic strain of the cell; while the bias stress tensor causes the full plastic strain of the cell. The expression is as follows:
Figure BDA0002951932350000031
Sij＝σii-σm
wherein sigma11，σ22，σ33Showing principal stresses in three directions.
Step (3.2) establishing a yield relation of the metal materials:
in this section, the Mises yield criterion is used as a criterion, and the Mises equivalent stress is used to judge whether the material enters a yield stage (plastic stage), wherein the expression of the Mises equivalent stress is as follows:
Figure BDA0002951932350000032
in the formula J2Is a second invariant of stress, which can be calculated from the bias stress tensor:
Figure BDA0002951932350000033
the yield function of the Mises criterion is:
f＝σmises-σy
sigma in the formulayIs the current yield stress, i.e. the plastic flow stress of the constitutive equation of the metallic material
Figure BDA0002951932350000034
If f<0, indicating that the material unit is still in the elastic stage; if f>0, the material unit has already yielded and enters the plastic phase. At this point, the previous elastic trial stress σ must be appliedtrAnd (4) reducing according to the scale coefficient m by using a radial return method, returning to the yield surface, and calculating the real stress size. According to the elasto-plastic mechanics theory, the equivalent plastic strain increment delta epsilon of the increment stepplCan be expressed as follows:
Figure BDA0002951932350000035
wherein,
Figure BDA0002951932350000036
is the yield stress at the end of the incremental step, i.e. the new flow stress; m is a reduced scale factor.
Figure BDA0002951932350000037
The formula of the aluminum material described by the modified constitutive model is as follows:
Figure BDA0002951932350000038
step (3.3) establishing a damage failure relation of the sheet metal component:
the Johnson-cook shear failure criterion is adopted as a criterion, the shear failure criterion is suitable for the deformation of high strain and high strain rate of metal, the failure characteristics of the material can be well expressed, and the empirical formula is as follows:
Figure BDA0002951932350000041
γ＝-σp/σmises
in the formula:
Figure BDA0002951932350000042
equivalent plastic strain at the initial position of failure;
Figure BDA0002951932350000043
is the equivalent plastic strain rate; gamma is the triaxial stress, sigmapIs compressive stress, σmisesIs the Misses stress; d1-d5Is the toughness failure parameter of the material.
When equivalent plastic strain accumulation reaches
Figure BDA0002951932350000044
At that time, the material unit will begin to enter a failure phase. Therefore, a state variable ω is defined, representing the equivalent plastic strain of the material
Figure BDA0002951932350000045
And initial strain to failure
Figure BDA0002951932350000046
The expression of the ratio of (a) to (b) is:
Figure BDA0002951932350000047
when omega is larger than or equal to 1, the material begins to enter a failure evolution stage, and along with the failure evolution, the material unit completely fails until the unit deletion occurs.
The step (4) is specifically as follows:
combining the model main file established in the step (1) with the ABAQUS-VUMAT user subprogram established in the step (2) and the step (3), and calculating the laser shock forming sheet metal component by using an ABAQUS explicit solving method to obtain the mechanical behavior of material failure; then, by using the strain rate change criterion, namely that the strain rate of the material is changed sharply at the breaking moment in the bulging and breaking process, we determine that the material is subjected to buckling failure, and take the limit values of the first main strain and the second main strain of the material at the previous analysis step of the buckling failure as the limit strains of the material under a specific impact load. And analyzing the sizes of different workpieces to obtain different limit strain values of the material, thereby finally obtaining the forming limit of the sheet metal component.
Advantageous effects
Compared with the prior art, the invention has the beneficial effects that:
1. a gaussian distributed impact load suitable for laser impact forming is provided.
2. The established material rate related elastic-plastic constitutive model considers the influence of strain rate sensitivity of the sheet metal component in the laser shock high strain rate forming process.
3. The modified Johnson-cook constitutive model is numerically realized by using an ABAQUS-VUMAT user subprogram, and the mechanical behavior of the failure of the sheet metal component under Gaussian distribution impact load can be accurately predicted.
4. And (3) predicting the forming limit of the material by taking the strain state of the previous analysis step, namely wrinkling of the material, according to the strain rate change criterion, namely that the strain rate of the material is changed sharply at the failure moment.
5. The invention utilizes the subprogram to establish a correction model to predict the high strain rate forming method more suitable for laser, wherein the high strain rate sensitivity is considered, and the laser impact micro-forming limit diagram is predicted based on the subprogram developed above.
6. The forming limit of the sheet metal component is predicted by utilizing the established finite element model, and the given forming limit diagram has good reference value for researching the forming property of the sheet metal component in laser dynamic high strain rate forming.
Drawings
FIG. 1 is a diagram of a finite element model used in the present invention;
FIG. 2 is a flow chart of the present invention for implementing VUMAT values for proposed rate-dependent elasto-plastic constitutive models and failure models;
FIG. 3 is a graph of predicted forming failure stress distributions for the example of FIG. 2;
FIG. 4 is a graph of the results of predicting strain rate versus time for the example of FIG. 2;
fig. 5 is a graph of predicted forming limits for the example of fig. 2.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the drawings are illustrative and intended to be illustrative of the invention and are not to be construed as limiting the invention.
The invention is described in further detail below with reference to the following detailed description and accompanying drawings:
a high-speed impact quarter symmetry model of a sheet metal element is established in ABAQUS/CAE on the basis of its symmetry, which, as shown in connection with figure 1, is disc-shaped with a radius of 2 mm. Securing the sides of the sheet metal, two halves in the middleThe radial surfaces each impose a corresponding symmetry constraint. The metal material is aluminum, and the density is 2710kg/m3The elastic modulus E is 72GPa, the Poisson ratio mu is 0.33, the metal plate is discretized by a reduction-integration three-dimensional eight-node solid unit C3D8R, the unit size of the metal plate is 0.008mm, and the impact load type is a Gaussian distribution load and acts on the central area of the disc.
Establishing an elastoplasticity mechanical relationship of the metal material:
defined by the material model, the strain rate and total strain can be decomposed into an elastic part and a plastic part:
dε＝dεel+dεpl
ε＝εel+εpl
wherein epsilonelIs an elastic strain; epsilonplRepresenting plastic strain.
According to the radial return method, it is first assumed that the material elements are still in the elastic phase, and the strains that occur are all elastic strains, i.e. Δ ∈ ═ Δ ∈e. The elastic deformation is assumed to be linearly isotropic, and the relationship between the bulk modulus λ and the shear modulus G and young's modulus E is:
Figure BDA0002951932350000061
Figure BDA0002951932350000062
wherein ν is the poisson's ratio.
In general, the stress of a metal material can be decomposed into a spherical stress tensor (hydrostatic stress) σmSum bias stress tensor SijTwo parts. Wherein the global stress tensor induces the full elastic strain of the cell; while the bias stress tensor causes the full plastic strain of the cell. The expression is as follows:
Figure BDA0002951932350000063
Sij＝σii-σm
wherein sigma11，σ22，σ33Showing principal stresses in three directions.
Considering the yield relationship of metallic materials:
in this section, the Mises yield criterion is used as a criterion, and the Mises equivalent stress is used to judge whether the material enters a yield stage (plastic stage), wherein the expression of the Mises equivalent stress is as follows:
Figure BDA0002951932350000064
in the formula J2Is a second invariant of stress, which can be calculated from the bias stress tensor:
Figure BDA0002951932350000065
the yield function of the Mises criterion is:
f＝σmises-σy
sigma in the formulayIs the current yield stress, i.e. the plastic flow stress of the constitutive equation of the metallic material
Figure BDA0002951932350000066
If f<0, indicating that the material unit is still in the elastic stage; if f>0, the material unit has already yielded and enters the plastic phase. At this point, the previous elastic trial stress σ must be appliedtrAnd (4) reducing according to the scale coefficient m by using a radial return method, returning to the yield surface, and calculating the real stress size. According to the elasto-plastic mechanics theory, the equivalent plastic strain increment delta epsilon of the increment stepplCan be expressed as follows:
Figure BDA0002951932350000067
wherein,
Figure BDA0002951932350000071
is the yield stress at the end of the incremental step, i.e. the new flow stress; m is a reduced scale factor.
Figure BDA0002951932350000072
The formula of the aluminum material described by the modified constitutive model is as follows:
Figure BDA0002951932350000073
establishing a damage failure relation of the metal material:
the Johnson-cook shear failure criterion is adopted as a criterion, the shear failure criterion is suitable for the deformation of high strain and high strain rate of metal, the failure characteristics of the material can be well expressed, and the empirical formula is as follows:
Figure BDA0002951932350000074
γ＝-σp/σmises
in the formula:
Figure BDA0002951932350000075
equivalent plastic strain at the initial position of failure;
Figure BDA0002951932350000076
is the equivalent plastic strain rate; gamma is the triaxial stress, sigmapIs compressive stress, σmisesIs the Misses stress; d1-d5Is the toughness failure parameter of the material.
When equivalent plastic strain accumulation reaches
Figure BDA0002951932350000077
At that time, the material unit will begin to enter a failure phase.Therefore, a state variable ω is defined, representing the equivalent plastic strain of the material
Figure BDA0002951932350000078
And initial strain to failure
Figure BDA0002951932350000079
The expression of the ratio of (a) to (b) is:
Figure BDA00029519323500000710
when omega is larger than or equal to 1, the material begins to enter a failure evolution stage, and along with the failure evolution, the material unit completely fails until the unit deletion occurs.
Finally, the strain rate change analysis is carried out on the dynamic stress state obtained from the ABAQUS/EXPLICIT, and as shown in FIG. 4, the stress strain state of the thin plate metal member before failure is determined, so that the forming limit strain value of the thin plate metal member is obtained.
Referring to fig. 3, the results of the stress distribution of failure of the sheet metal member under the impact of the laser gaussian distributed load can be seen, and at the edges of maximum stress, the wrinkling effect of the sheet member can be seen, and the material has failed.
With reference to fig. 4, it can be seen that the strain rate of the sheet metal member changes with time during the deformation process, and when the material fails, the member may have a sudden strain rate change, so that the wrinkling state of the material can be judged, and further the forming limit of the material can be predicted.
Referring to fig. 5, which is a forming limit diagram obtained at different material sizes, it can be seen that the forming limit of the material is predicted by using the primary strain and the secondary strain calculated near the crack region, and in order to generate a failure in a wide range of strain ratios, the deformation of samples of different sizes is simulated, and when the laser impacts the failure portion of the formed material, the primary strain is found to be positive, and the secondary strain is found to be negative, so that only a forming limit curve smaller than 0 is plotted.
The strain rate related elastoplasticity constitutive model provided by the invention considers the influence of strain rate sensitivity in laser impact high strain rate forming, combines a modified constitutive equation and a failure equation suitable for laser impact high strain rate forming, utilizes FORTRAN language to write a subprogram and embeds the subprogram into ABAQUS, can accurately predict the forming limit of a metal member under the laser impact forming condition, and plays a role in promoting the research of forming failure mechanical behavior of the metal member under an impact load.
In the description herein, references to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention, and that variations, modifications, substitutions and alterations can be made in the above embodiments by those of ordinary skill in the art without departing from the principle and spirit of the present invention.

Claims (6)

1. A finite element method for predicting the material mechanical behavior of a laser impact forming limit under an impact load is characterized by comprising the following steps:
step 1: establishing a finite element model of damage failure of the sheet metal component under the Gaussian distribution impact load;
step 2: establishing a material rate related hybrid hardening elastoplasticity constitutive model comprehensively considering strain hardening, strain rate strengthening and high strain rate sensitivity;
and step 3: the method comprises the following steps of writing ABAQUS/VUMAT by using FORTRAN language, namely an ABAQUS user dynamic material subprogram module, and realizing the proposed elastoplasticity constitutive model by using a central difference algorithm;
and 4, step 4: and embedding the subprogram into ABAQUS, calculating the high strain rate forming process of the laser impact sheet metal member, and further predicting the mechanical behavior of the sheet metal member, wherein the forming limit of the sheet metal member can be judged by utilizing a maximum strain rate criterion.
2. The finite element method for predicting the material mechanical behavior of the laser impact forming limit under the impact load according to claim 1, wherein the step 1 is specifically as follows:
firstly, establishing a finite element model of a sheet metal component; secondly, setting the material property of the sheet metal component; then, setting analysis step time according to the pulse width of the laser, and applying Gaussian distribution impact load to the sheet metal component after the analysis step is set; and finally, dividing the grid and submitting the operation.
3. A finite element method of predicting the limit mechanical behavior of laser shock formed under shock load according to claim 2, wherein during creating the finite element model of the sheet metal member, a corresponding time pressure profile is generated according to the laser pulse width in Python language.
4. A finite element method for predicting the mechanical behavior of a laser shock formed limit material under a shock load according to claim 1, wherein the step 2 is specifically:
under the condition of high strain rate, simulating laser dynamic forming by using a Johnson-cook constitutive model to underestimate flow stress, enlarging the sensitivity of the material in a high strain rate range, modifying the Johnson-cook constitutive model so as to be suitable for the working condition of laser dynamic high strain rate forming, wherein the modified model is as follows:
Figure FDA0002951932340000011
wherein A isYield strength in quasi-static state; b is a strain strengthening coefficient; ε is the plastic strain; epsilon0Is a reference strain; n is the strain hardening coefficient; c is a strain rate strengthening coefficient;
Figure FDA0002951932340000012
is the critical strain rate;
Figure FDA0002951932340000013
is a reference strain rate;
Figure FDA0002951932340000014
is the strain rate; m is a strain rate sensitivity coefficient; ln is logarithmic.
5. The finite element method of material mechanical behavior for predicting the laser shock forming limit under shock load according to claim 1, wherein the step 3 is specifically as follows:
step (3.1) establishing an elastoplasticity mechanical relationship of the metal material:
defined by the material model, the strain rate and total strain can be decomposed into an elastic part and a plastic part:
dε＝dεel+dεpl
ε＝εel+εpl
wherein epsilonelIs an elastic strain; epsilonplRepresenting the plastic strain;
according to the radial return method, it is first assumed that the material elements are still in the elastic phase, and the strains that occur are all elastic strains, i.e. Δ ∈ ═ Δ ∈e(ii) a The elastic deformation is assumed to be linearly isotropic, and the relationship between the bulk modulus λ and the shear modulus G and young's modulus E is:
Figure FDA0002951932340000021
Figure FDA0002951932340000022
wherein ν is the poisson's ratio;
for the stress of a metal material, it can be decomposed into a spherical stress tensor (hydrostatic stress) σmSum bias stress tensor SijTwo parts; wherein the global stress tensor induces the full elastic strain of the cell; while the bias stress tensor causes the full plastic strain of the cell; the expression is as follows:
Figure FDA0002951932340000023
Sij＝σii-σm
wherein sigma11，σ22，σ33Representing principal stresses in three directions;
step (3.2) establishing a yield relation of the metal materials:
in this section, the Mises yield criterion is used as a criterion, and the Mises equivalent stress is used to judge whether the material enters a yield stage (plastic stage), wherein the expression of the Mises equivalent stress is as follows:
Figure FDA0002951932340000024
in the formula J2Is a second invariant of stress, which can be calculated from the bias stress tensor:
Figure FDA0002951932340000025
the yield function of the Mises criterion is:
f＝σmises-σy
sigma in the formulayIs the current yield stress, i.e. the plastic flow stress of the constitutive equation of the metallic material
Figure FDA0002951932340000026
If f<0, indicating that the material unit is still in the elastic stage; if f>0, the material unit has already yielded and enters the plastic phase. At this point, the previous elastic trial stress σ must be appliedtrAnd (4) reducing according to the scale coefficient m by using a radial return method, returning to the yield surface, and calculating the real stress size. According to the elasto-plastic mechanics theory, the equivalent plastic strain increment delta epsilon of the increment stepplCan be expressed as follows:
Figure FDA0002951932340000031
wherein,
Figure FDA0002951932340000032
is the yield stress at the end of the incremental step, i.e. the new flow stress; m is a reduced scale factor;
Figure FDA0002951932340000033
the formula of the aluminum material described by the modified constitutive model is as follows:
Figure FDA0002951932340000034
step (3.3) establishing a damage failure relation of the metal material:
the Johnson-cook shear failure criterion is adopted as a criterion, the shear failure criterion is suitable for the deformation of high strain and high strain rate of metal, the failure characteristics of the material can be well expressed, and the empirical formula is as follows:
Figure FDA0002951932340000035
γ＝-σp/σmises
in the formula:
Figure FDA0002951932340000036
equivalent plastic strain at the initial position of failure;
Figure FDA0002951932340000037
is the equivalent plastic strain rate; gamma is the triaxial stress, sigmapIs compressive stress, σmisesIs the Misses stress; d1～d4Is a toughness failure parameter of the material;
when equivalent plastic strain accumulation reaches
Figure FDA0002951932340000038
At the same time, the material unit will start to enter the failure stage; therefore, a state variable ω is defined, representing the equivalent plastic strain of the material
Figure FDA0002951932340000039
And initial strain to failure
Figure FDA00029519323400000310
The expression of the ratio of (a) to (b) is:
Figure FDA00029519323400000311
when omega is larger than or equal to 1, the material begins to enter a failure evolution stage, and along with the failure evolution, the material unit completely fails until the unit deletion occurs.
6. The finite element method of material mechanical behavior for predicting the laser shock forming limit under shock load according to claim 1, wherein the step (4) is specifically as follows:
combining the model main file established in the step (1) with the ABAQUS-VUMAT user subprogram established in the step (2) and the step (3), and calculating the laser shock forming sheet metal component by using an ABAQUS explicit solving method to obtain the mechanical behavior of material failure; then, by utilizing a strain rate change criterion, namely that the strain rate of the material is changed sharply at the rupture moment in the bulging rupture process, we determine that the material is subjected to buckling failure, and take the limit values of the first main strain and the second main strain of the material under the previous analysis step of the buckling failure as the limit strains of the material under a specific impact load; different limit strain values of the material are obtained by analyzing the sizes of different workpieces, so that the forming limit of the material is finally obtained.
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CN113654711A (en) * 2021-07-22 2021-11-16 西安交通大学 Method for measuring peak pressure of Gaussian nanosecond pulse laser induced shock wave
CN114201897A (en) * 2021-12-06 2022-03-18 上海交通大学 Metal sheet edge cracking prediction considering blanking history
CN114218671A (en) * 2021-12-06 2022-03-22 西北工业大学 Numerical method for evaluating accumulated damage of metal frame structure due to multiple impacts
CN117094114A (en) * 2022-12-22 2023-11-21 北京强度环境研究所 Numerical calculation method for upper and lower limit loads of plastic stability of ideal elastic-plastic sheet

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109558692A (en) * 2018-12-25 2019-04-02 中国石油大学(华东) Predict the finite element method of metal component residual stress and martensitic traoformation under particle high speed impact
CN109946006A (en) * 2019-01-17 2019-06-28 中国石油大学(华东) Particle stream based on Mixed hardening impacts metal material mechanics behavior prediction method
CN111985131A (en) * 2020-08-10 2020-11-24 北京航空航天大学 Turbine mortise laser shock peening numerical simulation method considering curved surface shape

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109558692A (en) * 2018-12-25 2019-04-02 中国石油大学(华东) Predict the finite element method of metal component residual stress and martensitic traoformation under particle high speed impact
CN109946006A (en) * 2019-01-17 2019-06-28 中国石油大学(华东) Particle stream based on Mixed hardening impacts metal material mechanics behavior prediction method
CN111985131A (en) * 2020-08-10 2020-11-24 北京航空航天大学 Turbine mortise laser shock peening numerical simulation method considering curved surface shape

Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113642117A (en) * 2021-07-01 2021-11-12 中铝材料应用研究院有限公司 Prediction method of metal plate forming limit diagram
CN113654711A (en) * 2021-07-22 2021-11-16 西安交通大学 Method for measuring peak pressure of Gaussian nanosecond pulse laser induced shock wave
CN114201897A (en) * 2021-12-06 2022-03-18 上海交通大学 Metal sheet edge cracking prediction considering blanking history
CN114218671A (en) * 2021-12-06 2022-03-22 西北工业大学 Numerical method for evaluating accumulated damage of metal frame structure due to multiple impacts
CN117094114A (en) * 2022-12-22 2023-11-21 北京强度环境研究所 Numerical calculation method for upper and lower limit loads of plastic stability of ideal elastic-plastic sheet

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