CN113742934B - Method for establishing ferrite austenite duplex stainless steel constitutive model by considering martensitic transformation - Google Patents
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- 229910001566 austenite Inorganic materials 0.000 title claims abstract description 69
- 229910000859 α-Fe Inorganic materials 0.000 title claims abstract description 67
- 229910001039 duplex stainless steel Inorganic materials 0.000 title claims abstract description 25
- 229910000734 martensite Inorganic materials 0.000 title claims abstract description 23
- 230000009466 transformation Effects 0.000 title claims abstract description 20
- 238000000034 method Methods 0.000 title claims abstract description 13
- 230000004888 barrier function Effects 0.000 claims abstract description 8
- 230000035882 stress Effects 0.000 claims description 73
- 230000008646 thermal stress Effects 0.000 claims description 22
- 238000007725 thermal activation Methods 0.000 claims description 19
- 238000001994 activation Methods 0.000 claims description 8
- 230000004913 activation Effects 0.000 claims description 7
- 238000005482 strain hardening Methods 0.000 claims description 7
- 239000000463 material Substances 0.000 claims description 6
- 238000002474 experimental method Methods 0.000 claims description 5
- 239000013078 crystal Substances 0.000 claims description 4
- 230000035945 sensitivity Effects 0.000 claims description 4
- 230000001419 dependent effect Effects 0.000 claims description 2
- 239000012530 fluid Substances 0.000 claims description 2
- 230000004044 response Effects 0.000 claims description 2
- 230000006641 stabilisation Effects 0.000 claims description 2
- 238000011105 stabilization Methods 0.000 claims description 2
- 230000006835 compression Effects 0.000 claims 1
- 238000007906 compression Methods 0.000 claims 1
- 229910001220 stainless steel Inorganic materials 0.000 abstract description 11
- 239000010935 stainless steel Substances 0.000 abstract description 11
- 238000005520 cutting process Methods 0.000 abstract description 3
- 230000003993 interaction Effects 0.000 abstract description 3
- 238000004088 simulation Methods 0.000 abstract description 2
- 238000010587 phase diagram Methods 0.000 description 3
- 238000011160 research Methods 0.000 description 3
- VEXZGXHMUGYJMC-UHFFFAOYSA-N Hydrochloric acid Chemical compound Cl VEXZGXHMUGYJMC-UHFFFAOYSA-N 0.000 description 2
- 238000010586 diagram Methods 0.000 description 2
- 230000000694 effects Effects 0.000 description 2
- 230000007246 mechanism Effects 0.000 description 2
- VNWKTOKETHGBQD-UHFFFAOYSA-N methane Chemical compound C VNWKTOKETHGBQD-UHFFFAOYSA-N 0.000 description 2
- 230000008569 process Effects 0.000 description 2
- 239000013535 sea water Substances 0.000 description 2
- VEXZGXHMUGYJMC-UHFFFAOYSA-M Chloride anion Chemical compound [Cl-] VEXZGXHMUGYJMC-UHFFFAOYSA-M 0.000 description 1
- 229910000885 Dual-phase steel Inorganic materials 0.000 description 1
- 244000137852 Petrea volubilis Species 0.000 description 1
- 238000010276 construction Methods 0.000 description 1
- 229910000365 copper sulfate Inorganic materials 0.000 description 1
- ARUVKPQLZAKDPS-UHFFFAOYSA-L copper(II) sulfate Chemical compound [Cu+2].[O-][S+2]([O-])([O-])[O-] ARUVKPQLZAKDPS-UHFFFAOYSA-L 0.000 description 1
- 230000007797 corrosion Effects 0.000 description 1
- 238000005260 corrosion Methods 0.000 description 1
- 238000010612 desalination reaction Methods 0.000 description 1
- 239000012153 distilled water Substances 0.000 description 1
- 238000009826 distribution Methods 0.000 description 1
- 238000011156 evaluation Methods 0.000 description 1
- 239000003337 fertilizer Substances 0.000 description 1
- PCHJSUWPFVWCPO-UHFFFAOYSA-N gold Chemical compound [Au] PCHJSUWPFVWCPO-UHFFFAOYSA-N 0.000 description 1
- 239000010931 gold Substances 0.000 description 1
- 229910052737 gold Inorganic materials 0.000 description 1
- 238000010438 heat treatment Methods 0.000 description 1
- 239000007788 liquid Substances 0.000 description 1
- 238000004519 manufacturing process Methods 0.000 description 1
- 239000011159 matrix material Substances 0.000 description 1
- 239000007769 metal material Substances 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 239000003345 natural gas Substances 0.000 description 1
- 238000005498 polishing Methods 0.000 description 1
- 238000011084 recovery Methods 0.000 description 1
- 238000001953 recrystallisation Methods 0.000 description 1
- 238000007670 refining Methods 0.000 description 1
- 239000000126 substance Substances 0.000 description 1
- XLYOFNOQVPJJNP-UHFFFAOYSA-N water Chemical compound O XLYOFNOQVPJJNP-UHFFFAOYSA-N 0.000 description 1
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Abstract
A method for establishing a constitutive model of a ferritic austenitic duplex stainless steel taking martensitic transformation into consideration. Including establishing a velocity independent interaction force (non-thermally activated stress) between atoms, also a relationship of forces across the grain boundary barrier; and (3) establishing stress relation deduction related to the ferrite austenitic duplex stainless steel based on the MTS constitutive model. The transformation factor of austenite to martensite under the condition of lower strain rate is considered, so that the compressive strength and stress strain characteristics of the ferrite-austenite duplex stainless steel can be reflected more reasonably, and the analysis of the cutting process and the actual engineering problem is more reasonable. The viscous stress term generated by high strain rate is added on the basis of the MTS constitutive model, so that the original strain rate range of the constitutive equation is widened, and the corresponding high-speed cutting process is more reasonable in analysis. The built diphase stainless steel constitutive model has simple and easily-measured parameters, and is convenient to apply in finite element simulation.
Description
Technical Field
The invention belongs to the technical field of constitutive models of metal materials, and particularly relates to a method for establishing a ferrite austenitic duplex stainless steel constitutive model taking martensitic transformation into consideration.
Background
The duplex stainless steel is used as a very important material in the mechanical manufacturing industry, and has the advantages of ferrite stainless steel and austenite stainless steel by properly controlling chemical components and heat treatment process due to the characteristics of the two-phase structure, and combines the excellent toughness and weldability of the austenite stainless steel with the higher strength and chloride stress corrosion resistance of the ferrite stainless steel. Has been widely used in pulp and paper industry, petrochemical and fertilizer industry, food and light industry, transportation industry, oil refining and natural gas industry, construction industry in seawater environment, seawater desalination and energy environment protection industry.
At present, research on the constitutive model of stainless steel mainly focuses on stainless steel with relatively simple crystal structures of ferrite stainless steel and austenite stainless steel, but little research is done on the constitutive model of ferrite austenitic duplex stainless steel with relatively complex crystal structures. Therefore, it is very significant to propose a new viscoplastic dynamic constitutive model for duplex stainless steel on the basis of previous work.
The structure is based on the transformation of a microscopic plastic deformation control mechanism and a thermal activation dislocation dynamics theory, and comprehensively considers the common influence of related macroscopic factors (such as temperature, strain rate and the like) and partial microscopic factors (such as grain size, lattice type, dislocation distribution and type, dynamic recovery and dynamic recrystallization, martensitic transformation, deformation activation energy and the like). The viscous stress term generated by high strain rate is added on the basis of the MTS constitutive model, so that the original strain rate range of the constitutive equation is widened, and the corresponding high-speed cutting process is more reasonable in analysis. The built diphase stainless steel constitutive model has simple and easily-measured parameters, and is convenient to apply in finite element simulation.
Disclosure of Invention
In order to facilitate evaluation of performance changes under dynamic conditions and characteristics of materials cut at high speed, the present invention provides a method for establishing a constitutive model of ferritic austenitic duplex stainless steel taking into consideration martensitic transformation, the method comprising the steps of,
1) Dividing the flow stress of the total ferrite austenite duplex stainless steel into three parts, namely non-thermal stress, thermal stress and viscous stress; 2) Respectively establishing stress of three parts of each of a ferrite item and an austenite item according to the duplex attribute of the ferrite-austenite duplex stainless steel; 3) Firstly establishing interaction force (non-thermal activation stress) between atoms which is irrelevant to the speed on the basis of 2), and the interaction force is also a relational expression of force crossing a grain boundary barrier;
4) And establishing a thermal stress term based on the MTS constitutive model, wherein the thermal stress term of the austenite term needs to consider the influence of martensite transformation. Thereby correcting the thermal stress in the austenite item;
5) Adding a viscous stress term at a high strain rate;
6) And (3) mixing the content proportion of the two phases as a coefficient, and superposing to obtain the constitutive model of the ferrite austenitic duplex stainless steel.
In step 1), the equation is first divided into three parts
σ＝σa+σb+σc
Wherein σ is the flow stress; σ a is the non-heat activated resistance, length Cheng Shilei, dislocation grain boundaries; σ b is the thermal activation term, short Cheng Shilei; sigma c is viscous dragMu is the fluid viscosity.
Because the temperature is higher at high strain rates, the time to cross the short-range barrier (heat-activation related barrier resistance) is negligible at high strain rates, and σ b =0 at this time. Below this critical strain value σ c =0. As shown in fig. 2, the flow stress of duplex stainless steel increases with increasing strain rate, there is a critical strain value z such that the flow stress increases rapidly after the strain value is greater than z, at which point the graph is divided into two regions, σ=σ a+σb in the first region and σ=σ a+σc in the second region.
In step 2), the ferrite stresses and austenite stresses should be calculated and the proportioning weights should be added up, respectively, because of the two-phase nature of the material. The equation can be written as:
σ1＝σ1a+σ1b+σ1c
σ2＝σ2a+σ2b+σ2c
σ＝k1σ1+k2σ2
wherein k 1 is the proportion of ferrite; k 2 is the proportion of austenite; σ 1 is ferrite phase stress; σ 1a is ferrite non-heat activated stress; σ 1b is ferrite heat-activated stress; σ 1c is ferrite viscous stress; σ 2 is the austenite response; σ 2a is the austenite non-heat activated stress; σ 2b is the austenite heat activation stress; σ 2c is the austenite adhesion stress.
Step 3) is performed on the basis of step 2) to build ferrite phase stress, wherein ferrite phase is taken as a typical BCC structure phase, and the non-heat activation stress sigma 1a of ferrite phase stress can be expressed according to Hall-Petch formula (because ferrite is low in work hardening rate and easy to soften, the influence of strain rate and temperature on ferrite work hardening term is negligible. So it is counted as a non-thermal stress term):
Wherein K 1 is the ferrite strain hardening coefficient; n 1 is the ferrite strain rate sensitivity index; epsilon is the true strain; σ i1 is the total resistance to which dislocations are subjected during ferrite movement, which corresponds substantially to single crystal yield stress; d 1 is ferrite grain size; m 1 is a constant characterizing the extent of influence of ferrite grain boundaries on strength, and is related to ferrite grain boundary structure, and can be determined by the slope of an experimental yield stress-grain size relationship curve.
Performing step 4) on the basis of step 2) the thermal activation stress σ 1b of the ferrite phase may be expressed in terms of a thermal activation function multiplied by a thermal stress term.
The thermal activation function is:
wherein k is a Boltzmann constant; t is the temperature; Is the strain rate; p and q are a pair of associated constant parameters that determine the barrier shape; g 0 is the reference thermal activation energy; /(I) Is the reference strain rate. Wherein m is Schmidt direction factor, b is Burgers vector of dislocation; ρ d is the mobile dislocation density and v 0 is the dislocation motion speed.
The ferrite thermal stress term σ h1 is:
Wherein, Is a reference value for ferrite saturation threshold stress at t=0k; e is the shear modulus of the material; a 0 is a constant. The ferrite phase heat activation stress σ 1b should be expressed as:
the viscous stresses of the ferrite phase austenitic phase of step 5) performed on the basis of step 2) are considered to be the same, so
So ferrite phase stress σ 1 is:
Step 2) the austenitic phase is then used as a typical FCC structural phase, whose non-heat activated stress σ 2a can be expressed according to the Hall-Petch formula:
Wherein σ i2 is the total resistance experienced by dislocations as they move within austenite; d 2 is austenite grain size; m 2 is a constant characterizing the extent of influence of austenite grain boundaries on strength, and is related to austenite grain boundary structure, and can be determined by the slope of the experimental yield stress-grain size relationship curve.
The heat-activated stress of the austenite phase is similar to ferrite, and σ 2b can be expressed in terms of the heat-activated function multiplied by the heat-activated stress term. The same heat activation function, the thermal stress term before modification (the work hardening rate of austenite is high, easy to harden, the austenite hardening effect at this time should be added to the austenitic thermal stress term, and the martensite transformation is not considered at this time):
Wherein, Is a reference value for the austenite saturation threshold stress at t=0k; k 2 is the austenite strain hardening coefficient; n 2 is the austenite strain rate sensitivity index.
It is also considered that step 4) is performed on the basis of step 2) and that for austenite there is a martensitic transformation at a certain strain rate range. According to the research, the higher the strain rate, the smaller the transformation amount of martensite, so the transformation process of austenite into martensite can be disregarded at the time of high strain rate. However, there is a martensitic transformation in the range of strain rates under the heat activation mechanism. Because of the high yield strength, high flow stress (because martensite is harder than austenite) due to the transformation of austenite to martensite. Whereas the martensite and ferrite phases have almost the same lattice parameters. Therefore, the constitutive equation is built by the proportion weight of martensite according to the thermal stress term of ferrite lattice only by knowing the content of austenite converted into martensite.
The exponential relationship of austenite volume fraction and plastic deformation is as follows:
fγ＝fγ0e-rε
Wherein γ is a temperature dependent austenite stabilization parameter; f γ is the austenite volume fraction in real time; f γ0 is the initial austenite volume fraction. The modified thermal stress term for austenite-bonded martensitic transformation is:
the thermal activation stress σ 2b of the austenite phase should be expressed as:
So the austenite corresponding force sigma 2 is
Let BCC: let FCC: /(I) Let/>Let/>
Step 6) in summary, the flow stress σ of the duplex stainless steel obtained by combining the stress combination proportioning weights of the ferrite phase and the austenite phase can be expressed as:
Drawings
FIG. 1 is a flow chart of the building of the constitutive model;
FIG. 2 is a diagram of a method of using the constitutive model;
FIG. 3 is an identification of critical strain values and region divisions for stress spikes with increasing strain rate;
FIG. 4 is a microscopic golden phase diagram of S32760;
FIG. 5 is a graph of a comparison of a fitted stress-strain curve and an experimental true stress-strain curve of the constitutive model established at a strain rate of 10s -1;
FIG. 6 is a graph of a comparison of a fitted stress-strain curve and an experimental true stress-strain curve for a constitutive model established at a strain rate of 1000s -1;
Fig. 7 is a graph of comparison of a fitted stress-strain curve and an experimental true stress-strain curve of the constitutive model established at a strain rate of 10000s -1.
Detailed description of the preferred embodiments
In order to make the use method of the present invention clearer, the establishment of the constitutive model and the identification of parameters provided by the present invention are explained below with reference to the drawings and specific examples, and the present model is verified.
According to the constructed model, the following experiment is further carried out, and a typical austenitic ferrite dual-phase steel stainless steel S32760 is taken as an example, and the specific steps are as follows
Firstly, hopkinson pressure bar experiments under different strain rates are carried out on the S32760, and in order to obtain the mechanical property of the S32760 under dynamic conditions, the stress strain curve of the hopkinson pressure bar is determined under the conditions of 10S -1、100s-1、1000s-1、3000s-1、10000s-1 and the five strain rates. And (3) finding out a critical strain value for enabling the flow stress to be increased suddenly, and dividing the curve into areas so as to correctly use the established constitutive equation. As shown in fig. 3, the flow stress was σ=σ a+σb before the strain rate was 3000s -1, and after the strain rate was 3000s -1, the flow stress was σ=σ a+σc.
Further, the ferrite and austenite grain sizes and the phase volume fraction of the S32760 duplex stainless steel are observed and calculated, S32760 is prepared into a small sample, the small sample is polished by sand paper, polished by a polishing machine, and then put into a corrosive liquid prepared from 4g of copper sulfate, 20ml of hydrochloric acid and 20ml of distilled water to be etched for 35 seconds at room temperature, and then the metallographic structure diagram is observed under an electron microscope. The black matrix portion is a ferrite structure, the white island portion is an austenite structure, and the two phases are measured by comparing with a phase diagram to obtain a ratio, as shown in fig. 4.
Further, the determination of parameters of the constitutive model is performed through structural characteristics of BCC and FCC, corresponding structural parameters, empirical parameters of MTS constitutive model, stress-strain curves at different temperatures according to different strain rates of S32760, and analysis of S32760 microscopic gold phase diagrams.
Further, the accuracy of the constitutive model is verified, and the stress-strain curve formed by the constitutive model is compared with the experimental stress-strain curve of the corresponding strain rate, so that the fitting effect under the strain rate in a very wide range is good. Only the maximum strain rates 10000s -1 and the minimum strain rates 10s -1 and the intermediate strain rates 1000s -1 are shown here, and are shown in particular in fig. 5.
It will be evident to those skilled in the art that the invention is not limited to the details of the foregoing illustrative embodiments, and that the present invention may be embodied in other specific forms without departing from the spirit or essential characteristics thereof. The present embodiments are, therefore, to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein.
Claims (2)
1. A method of building a constitutive model of ferritic austenitic duplex stainless steel taking into account martensitic transformation, the method comprising the steps of:
1) Dividing the flow stress of the total ferrite austenite duplex stainless steel into three parts, namely non-thermal stress, thermal stress and viscous stress;
2) Respectively establishing stress of three parts of each of a ferrite item and an austenite item according to the duplex attribute of the ferrite-austenite duplex stainless steel;
3) Firstly establishing non-thermal activation stress between atoms irrelevant to speed on the basis of 2), and the non-thermal activation stress is also a relation of force crossing a grain boundary barrier;
4) Establishing a thermal stress term based on the MTS constitutive model, wherein the thermal stress term of the austenite term needs to consider the influence of martensitic transformation;
5) Thereby correcting the thermal stress in the austenite item;
6) Adding a viscous stress term at a high strain rate;
7) Mixing the content proportion of the two phases as a coefficient, and superposing to finally obtain the constitutive model of the ferrite austenitic duplex stainless steel;
8) Performing Hopkinson pressure bar experiments under different strain rates on the S32760;
9) Observing and calculating ferrite and austenite grain sizes and phase volume fractions of the S32760 duplex stainless steel;
10 Determining parameters of the constitutive model;
11 Verifying accuracy of the constitutive model;
in step 1), the equation is first divided into three parts
σ＝σa+σb+σc
Wherein σ is the flow stress; σ a is the non-heat activated resistance, length Cheng Shilei, dislocation grain boundaries; sigma b is the heat activated term, short Cheng Shilei Sigma c is viscous dragΜ is the fluid viscosity, since the temperature is higher at high strain rates, the time to cross the short range barrier is negligible at high strain rates, so σ b =0 at this time, σ c =0 below this critical strain rate value; the flow stress of duplex stainless steel increases with increasing strain rate, there is a critical strain rate value z, such that the flow stress increases sharply after the strain rate value is greater than z, and this time is divided into two regions, a first region σ=σ a+σb and a second region σ=σ a+σc;
In the step 2), three stresses of ferrite and three stresses of austenite are calculated respectively and proportioning weights are added up because of the biphase property of the material, and the equation is as follows:
σ1＝σ1a+σ1b+σ1c
σ2＝σ2a+σ2b+σ2c
σ＝k1σ1+k2σ2
wherein k 1 is the proportion of ferrite; k 2 is the proportion of austenite; σ 1 is ferrite phase stress; σ 1a is ferrite non-heat activated stress; σ 1b is ferrite heat-activated stress; σ 1c is ferrite viscous stress; σ 2 is the austenite response; σ 2a is the austenite non-heat activated stress; σ 2b is the austenite heat activation stress; σ 2c is the austenite adhesion stress;
step 3) is performed on the basis of step 2) to establish ferrite phase stress as a typical BCC structural phase, whose non-heat activated stress σ 1a is expressed according to the Hall-Petch formula:
wherein K 1 is the ferrite strain hardening coefficient; n 1 is the ferrite strain rate sensitivity index; epsilon is the true strain; σ i1 is the total resistance to which dislocations are subjected during ferrite movement, which corresponds substantially to single crystal yield stress; d 1 is ferrite grain size; m 1 is a constant representing the influence degree of ferrite grain boundary on strength, is related to ferrite grain boundary structure and is determined by the slope of an experimental yield stress-grain size relation curve;
Performing step 4) on the basis of step 2) that the thermal activation stress σ 1b of the ferrite phase is expressed in terms of a thermal activation function multiplied by a thermal stress term, the thermal activation function being:
wherein k is a Boltzmann constant; t is the temperature; Is the strain rate; p and q are a pair of associated constant parameters that determine the barrier shape; g 0 is the reference thermal activation energy; /(I) Is a reference strain rate, wherein m · is a Schmidt direction factor, and b is a Burgers vector of dislocation; ρ d is the mobile dislocation density, v 0 is the dislocation motion velocity, and ferrite thermal stress term σ h1 is:
Wherein, Is a reference value for ferrite saturation threshold stress at t=0k; e is the shear modulus of the material; σ 0 is a constant, so the ferrite phase thermal activation stress σ 1b is expressed as:
the viscous stresses of the ferrite phase austenitic phase of step 5) performed on the basis of step 2) are considered to be the same, so So ferrite phase stress σ 1 is:
Step 2) the austenitic phase is then established as a typical FCC structural phase, whose non-heat activated stress σ 2a is expressed according to the Hall-Petch formula:
Wherein σ i2 is the total resistance experienced by dislocations as they move within austenite; d 2 is austenite grain size; m 2 is a constant characterizing the extent of influence of austenite grain boundaries on strength, and is related to the austenite grain boundary structure, and is determined by the slope of an experimental yield stress-grain size relationship curve, the thermal activation stress of the austenite phase is similar to ferrite, sigma 2b is expressed by multiplying a thermal activation function by a thermal stress term, the thermal activation function is the same, and the thermal stress term before correction:
Wherein, Is a reference value for the austenite saturation threshold stress at t=0k; k 2 is the austenite strain hardening coefficient; n 2 is the austenite strain rate sensitivity index;
Step 4) is performed on the basis of step 2) and for austenite, the austenitic volume fraction has the following exponential relationship with plastic deformation:
fγ＝fγ0e-rε
Wherein γ is a temperature dependent austenite stabilization parameter; f γ is the austenite volume fraction in real time; f γ0 is the initial austenite volume fraction, so the corrected thermal stress term for austenite-bonded martensite phase transformation is:
The thermal activation stress σ 2b of the austenite phase is expressed as:
So the austenite corresponding force sigma 2 is
Let BCC:
let FCC: /(I) Let/>Let/>
Step 6) in summary, the flow stress sigma of the duplex stainless steel obtained by combining the stress combination proportioning weights of the ferrite phase and the austenite phase is expressed as follows:
2. the method for building the constitutive model of ferritic austenitic duplex stainless steel considering martensitic transformation according to claim 1, characterized in that: parameters of an constitutive equation of the typical ferrite austenitic duplex stainless steel of S32760 are determined through Hopkins compression bar experiments and metallographic experiments, and finally are substituted into the constitutive equation to be compared with actual experimental data, so that the result fitting is good.
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| 基于位错机制钛合金本构关系的目标参数识别及实验验证;盛鹰;曾祥国;陈华燕;韩悌信;;四川大学学报(工程科学版)(第06期);全文 * |
| 应变速率对不同强度级别TRIP钢力学行为影响的研究;何忠平;中国博士学位论文全文数据库(第05期);全文 * |
| 强动载荷下金属材料塑性变形本构模型评述;刘旭红;黄西成;陈裕泽;苏先樾;朱建士;;力学进展(第03期);全文 * |
| 数值模拟与热处理技术进步;谢建华;魏兴钊;黄鹏;;热处理技术与装备(第05期);全文 * |
| 金属塑性变形的本构模型研究;是晶;张伟强;郭金;;材料导报(第04期);全文 * |
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