CN106053222A - Fitting method of Johnson-Cook constitutive model of aluminium-silicon alloy ADC12 material - Google Patents

Abstract

The invention discloses a fitting method of a Johnson-Cook constitutive model of an aluminium-silicon alloy ADC12 material and aims to solve the problem that relevant parameters in Johnson-Cook constitutive models of ADC12 aluminium-silicon alloys of cylinder block and cylinder cover materials of gasoline engines are uncertain. According to the method, firstly, the model is decoupled, static and dynamic mechanical property tension and compression tests are performed, and relevant parameters of the decoupled model are fitted according to test data. With the method, the static and dynamic mechanical property tests are performed on the metal material, values of the parameters of the Johnson-Cook constitutive model of the die-cast aluminium-silicon alloy ADC12 material are obtained, an effective method is provided for research on static and dynamic mechanical properties of the metal material in the future, and a test basis is provided for high-speed cutting simulation research on the aluminium-silicon alloy ADC12 material.

Description

A kind of approximating method of alusil alloy ADC12 material Johnson-Cook constitutive model

Technical field

The invention belongs to the dynamic and static mechanics technical field of gasoline engine cylinder, cylinder head material, relate to a kind of aluminum silicon and close The approximating method of gold ADC12 material Johnson-Cook constitutive model.The method simulates aluminum silicon based on Hopkinson lever apparatus The Johnson-Cook Parameters of constitutive model of alloy ADC12 material.

Background technology

Electromotor is as part most important in automobile, its machining accuracy service behaviour and reliability to promoting electromotor Play key effect, in order to improve its machining accuracy, it is necessary first to the material of gray iron is studied, and to its material The research carrying out mechanical property is significant, and wherein, the determination of Johnson-Cook Parameters of constitutive model is the most important A ring, then need dynamic mechanical and the static mechanical property of this material are studied.

The dynamic mechanical of materialIt is the theoretical basis of research material cutting deformation, is also to it Carry out the essential condition of finite element cutting simulation analysis, and along with big strain, high strain-rate and height in high-speed machining process The feature of temperature, the dynamic mechanical therefore obtaining material becomes particularly important, is also the focus of research both at home and abroad.Material quiet State mechanical property σ=f (ε), can be obtained by common materials mechanics experimental.

Along with needing and the progress of science and technology of actual production, the most most of more common metal materials are carried out Sufficient research.And alusil alloy ADC12 is a kind of pack alloy, substantially by waste aluminum regeneration, its dynamic force Learn performance etc. to be difficult to be obtained by inspection information, and it is carried out cutting numerical value by whether accurate the affecting of this material constitutive model The correctness of simulation, it is therefore desirable to the mechanical property to ADC12 material by quasi-static test and Hopkinson bar dynamic test Can study, draw this material strain-stress relation under different temperatures, different strain rate, and then calculate and simulate Its Johnson-Cook constitutive relation model, then carries out validation verification to its constitutive model in finite element software.

Summary of the invention

For the deficiency of existing achievement in research, the present invention simulates alusil alloy ADC12 material based on Hopkinson lever apparatus Parameter in material Johnson-Cook (being called for short J-C) constitutive model, the matching of this parameter can be by entering alusil alloy material Mobile state and quasistatic mechanical property test draw its strain-stress relation, carry out calculating and simulate its J-C constitutive relation mould Type, then carries out validation verification to its constitutive model in finite element software.Its J-C constitutive relation model is

${\mathrm{\σ}}_{eq}=(A+{{\mathrm{B\ϵ}}_{eq}}^n)(1+C\ln \stackrel{\·}{{\mathrm{\ϵ}}_{eq}^{*}})(1-T^{*m})---\left(1\right)$

Wherein σ_eqFor Von Mises equivalent stress, A is material yield strength under reference strain rate and reference temperature, B, n are respectively strain hardening coefficient and hardenability value, ε_eqFor equivalent strain,For nondimensionalization equivalent ductility Strain,For equivalent strain rate,For with reference to strain rate, C is strain rate sensitivity coefficient, T^*m=(T-T_r)/(T_m-T_r) it is nothing Dimension temperature, wherein T_m、T_rBeing respectively fusing point and the reference temperature (taking room temperature) of material, T is Current Temperatures, and m is that temperature softens Coefficient.

For achieving the above object, the technical solution used in the present invention is as follows:

The approximating method of a kind of alusil alloy ADC12 material Johnson-Cook constitutive model, is a kind of based on Hope's gold Gloomy lever apparatus simulates the Johnson-Cook Parameters of constitutive model of alusil alloy ADC12 material, comprises the following steps:

The first step, decouples this Johnson-Cook constitutive model, respectively obtains strain hardening item σ_eq, strain rate hard Change item σ_eq, temperature soften item σ_eq:

${\mathrm{\σ}}_{eq}=A+{\mathrm{B\ϵ}}_{eq}^n---\left(2\right)$

${\mathrm{\σ}}_{eq}=A(1+{\mathrm{Cln\ϵ}}_{eq}^{*})---\left(3\right)$

σ_eq=A (1-T^*m) (4)

Second step, the strain rate size needed for testing according to dynamic mechanical, design and carry out the required examination of dynamic test The version of part and size, and process the test specimen of requirement and kind；Connect room temperature quasi-static test platform, Foil gauge in high temperature quasi-static test platform, Hopkinson lever apparatus and dynamic strain indicator；

Room temperature quasi-static test platform carries out the one directional tensile test under room temperature to test specimen, it is thus achieved that engineering stress-should Varied curve, respectively as it is shown in figure 1, draw its yield strength size at normal temperatures, thus obtains the value of A；

The test value obtained is obtained ture stress-strain by formula (5) (6)；

σ_t=σ_e(1+ε_e) (5)

ε_t=ln (1+ ε_e) (6)

Ture stress-strain utilize formula (7) carry out linear fit: ln (σ_t-A)=lnB+nln ε_t (7)

The matched curve obtained is as shown in Figure 2, it is thus achieved that the value of B and n in dependent variable；

3rd step, carries out organizing the tension test of different strain rate more at Hopkinson lever apparatus, in testing dynamic tensile The stress wave signal recorded is converted to ess-strain by formula (8),

$\left\{\begin{array}{c}\mathrm{\σ}\left(t\right)=E\left(\frac{A}{A_s}\right){\mathrm{\ϵ}}_T\left(t\right)\\ \mathrm{\ϵ}\left(t\right)=-\frac{2C_o}{L}{\∫}_0^t{\mathrm{\ϵ}}_R\left(t\right)dt\\ \mathrm{\ϵ}\left(t\right)=-\frac{2C_o}{L}{\mathrm{\ϵ}}_R\left(t\right)\end{array}\right.---\left(8\right)$

Can obtain final required engineering stress strain curve, true stress-strain curve and each self-corresponding should Variability, as shown in Figure 3.In formula (8): E is the elastic modelling quantity of bar material, A and A_sIt is respectively bar and the cross-sectional area of test specimen, C₀For Stress wave spread speed in bar, L is specimen length.Straining the yield stress in Fig. 3 utilizes method of least square to intend Conjunction processes, and can obtain the result of the test shown in Fig. 4, such that it is able to obtain the value of C in formula (3)；

4th step, carries out tension test to test specimen on high temperature quasi-static test platform, it is thus achieved that strain-stress relation bent Line is as shown in Figure 5.The stress intensity that the most each knee of curve is corresponding subtracts in notch cuttype along with the rising of temperature Little, illustrate that the flow stress of this material is obvious by temperature emollescence, utilize method of least square to surrender at each temperature in Fig. 5 Intensity is fitted, and obtains the curve in Fig. 6, and obtains the value of m in formula (4)；

From first to the 4th, step has obtained the extensograph parameter value of Johnson-Cook constitutive model.

5th step, due to the dependency of the stress state of material, stress under material stretching at normal temperatures and compression-loaded Strain stress relation presents bigger diversity, alusil alloy ADC12 material carries out under normal temperature condition quasistatic and dynamically presses Contracting test, draws related stress-strain curve, the most as shown in figures 7 and 9, and therefrom obtains bending under each strain rate Take intensity；The yield strength under the conditions of the quasistatic compression i.e. value of A can be obtained, utilize method of least square to quasistatic compression Test data is fitted the fitting result obtained as shown in Figure 8, can obtain the value of B and n in strain hardening item accordingly；

6th step, is fitted the dynamic compressive test result method of least square shown in Fig. 9, can obtain strain rate hardening The value of C in Xiang；

The compression test parameter value of Johnson-Cook constitutive model is obtained by the 5th step and the 6th step.

The method of the present invention, tests by metal material carries out static state and dynamic mechanical, obtains die casting aluminium silicon and close The value of the Johnson-Cook Parameters of constitutive model of gold ADC12 material, for carrying out static state and dynamic force to metal material later Learning performance study and provide effective method, aluminium alloy ADC12 material carries out high-speed cutting simulation study provides test basis.

Accompanying drawing explanation

Fig. 1 is room temperature quasi-tensile test result.

Fig. 2 is the test data result of the strain hardening item matching in J-C model.

Fig. 3 is dynamic tensile test structure.

Fig. 4 is the test data result of the strain rate item matching in J-C model.

Fig. 5 is high temperature quasi-tensile test result.

Fig. 6 is the test data result of the temperature term matching in J-C model.

Fig. 7 is room temperature quasistatic compression result of the test.

Fig. 8 is the strain hardening item fitting result in J-C model.

Fig. 9 is dynamic compressive test result.

Detailed description of the invention

The static state and the Research of dynamic mechanical that the present invention is directed to metal material propose a kind of simple and effective experimental study Method, and carried out test for the Johnson-Cook constitutive model of the following formula (1) of diecasting aluminum-silicon alloy ADC12 material and grind Study carefully:

${\mathrm{\σ}}_{eq}=(A+{{\mathrm{B\ϵ}}_{eq}}^n)(1+C{\mathrm{ln\ϵ}}_{eq}^{*})(1-T^{*m})---\left(1\right)$

The Johnson-Cook Parameters of constitutive model of alusil alloy ADC12 material is simulated based on Hopkinson lever apparatus, Comprise the following steps:

The first step, first decouples this J-C constitutive relation model, respectively obtains strain hardening item, strain rate hardening Item and temperature softening item:

${\mathrm{\σ}}_{eq}=A+{\mathrm{B\ϵ}}_{eq}^n---\left(2\right)$

${\mathrm{\σ}}_{eq}=A(1+{\mathrm{Cln\ϵ}}_{eq}^{*})---\left(3\right)$

σ_eq=A (1-T^*m) (4)

Second step, the strain rate size needed for testing according to dynamic mechanical, design and carry out the required examination of dynamic test The version of part and size, and process the test specimen of requirement and kind, wherein quasi-static tensile and dynamic tensile Test specimen；

3rd step, prepares test platform, connects room temperature quasistatic, high temperature quasi-static test platform and Hopkinson bar Foil gauge in test and the connection of dynamic strain indicator；

4th step, carries out the one directional tensile test under room temperature to test specimen, it is possible to obtain engineering on universal testing machine Load-deformation curve, respectively as it is shown in figure 1, draw its yield strength size at normal temperatures, such that it is able to obtain the value of A For 355.9MPa；

5th step, utilizes formula (5) (6) to obtain the true stress and strain curve obtained；

σ_t=σ_e(1+ε_e) (5)

ε_t=ln (1+ ε_e) (6)

Then true stress and strain curve utilizes formula (7) be fitted:

ln(σ_t-A)=lnB+nln ε_t (7)

Matched curve is as shown in Figure 2, it is possible to obtain the value of the B in dependent variable is that the value of 45.06MPa, n is 1.3141；

6th step, carries out organizing the tension test of different strain rate more, the stress wave signal recorded in testing dynamic tensile Ess-strain is converted to by formula (8),

$\left\{\begin{array}{c}\mathrm{\σ}\left(t\right)=E\left(\frac{A}{A_s}\right){\mathrm{\ϵ}}_T\left(t\right)\\ \mathrm{\ϵ}\left(t\right)=-\frac{2C_o}{L}{\∫}_0^t{\mathrm{\ϵ}}_R\left(t\right)dt\\ \mathrm{\ϵ}\left(t\right)=-\frac{2C_o}{L}{\mathrm{\ϵ}}_R\left(t\right)\end{array}\right.---\left(8\right)$

Final required engineering stress strain curve, true stress-strain curve and each self-corresponding strain can be obtained Rate, as shown in Figure 3.In formula (8): E is the elastic modelling quantity of bar material, A and A_sIt is respectively bar and the cross-sectional area of test specimen, C₀For answering Reeb spread speed in bar, L is specimen length.Straining the yield stress in Fig. 4 utilizes method of least square to be fitted Process, the result of the test shown in Fig. 4 can be obtained, such that it is able to the C value learnt in formula (3) is 0.00812；

7th step, the curves of stress-strain relationship that high temperature quasi-tensile test is obtained is as shown in Figure 5, it can be seen that The stress intensity that each knee of curve is corresponding reduces in notch cuttype along with the rising of temperature, illustrates that the flow stress of this material is by temperature Degree emollescence is obvious, utilizes method of least square to be fitted yield strength at each temperature in Fig. 5, obtains the song in Fig. 6 Line, and to obtain the value of m in formula (4) be 0.51481；

Therefore, each parameter value scope in formula (1) is as shown in Table 1 below.

The each parameter value of J-C constitutive model under table 1 stretching condition

A/MPa	B/MPa	C	n	m
					355.9	45.06	0.00812	1.3141	0.51481

8th step, due to the dependency of the stress state of material, stress under material stretching at normal temperatures and compression-loaded Strain stress relation presents bigger diversity, alusil alloy ADC12 material carries out under normal temperature condition quasistatic and dynamically presses Contracting test, draws related stress-strain curve, the most as shown in figures 7 and 9, and therefrom obtains bending under each strain rate Take intensity；Can obtain the yield strength under the conditions of quasistatic compression is 246.5MPa, utilizes method of least square to be directed at static pressure Contracting test data is fitted the fitting result obtained as shown in Figure 8, can obtain the B=775.09MPa in strain hardening item accordingly, N=0.77758；

9th step, is fitted the dynamic compressive test result method of least square shown in Fig. 9, can obtain strain rate hardening C=0.01252 in Xiang；

Therefore another class value of this material J-C Parameters of constitutive model can be obtained:

Under table 2 contractive condition each parameter value of J-C constitutive model

A/MPa	B/MPa	C	n	m
					246.5	775.09	0.01252	0.77758	0.51481

In sum, we have carried out tensile and compression test research to alusil alloy ADC12 material, and draw it respectively Material constitutive model parameter based on tensile and compression test, as shown in Table 1 and Table 2.

Claims (1)

1. an approximating method for alusil alloy ADC12 material Johnson-Cook constitutive model, its feature comprises the following steps:

The first step, decouples Johnson-Cook constitutive model, respectively obtains strain hardening item σ_eq, strain rate hardening item σ_eq, temperature soften item σ_eq:

${\mathrm{\σ}}_{eq}=A+{\mathrm{B\ϵ}}_{eq}^n---\left(2\right)$

${\mathrm{\σ}}_{eq}=A(1+{\mathrm{Cln\ϵ}}_{eq}^{*})---\left(3\right)$

σ_eq=A (1-T^*m) (4)

Second step, the strain rate size needed for testing according to dynamic mechanical, design and carry out test specimen needed for dynamic test Version and size, and process the test specimen of requirement and kind；Connect room temperature quasi-static test platform, high temperature Foil gauge in quasi-static test platform, Hopkinson lever apparatus and dynamic strain indicator；

Room temperature quasi-static test platform carries out the one directional tensile test under room temperature to test specimen, it is thus achieved that engineering stress-strain is bent Line, draws its yield strength size at normal temperatures, thus obtains the value of A；

The test value obtained is obtained ture stress-strain by formula (5) (6)；

σ_t=σ_e(1+ε_e) (5)

ε_t=ln (1+ ε_e) (6)

Ture stress-strain utilize formula (7) carry out linear fit, it is thus achieved that the value of B and n in dependent variable；

ln(σ_t-A)=lnB+nln ε_t (7)

3rd step, carries out organizing the tension test of different strain rate more at Hopkinson lever apparatus, records in testing dynamic tensile Stress wave signal be converted to ess-strain by formula (8), it is thus achieved that final required engineering stress strain curve, true stress Strain curve and each self-corresponding strain rate:

$\left\{\begin{array}{c}\mathrm{\σ}\left(t\right)=E\left(\frac{A}{A_s}\right){\mathrm{\ϵ}}_T\left(t\right)\\ \mathrm{\ϵ}\left(t\right)=-\frac{2C_o}{L}{\∫}_0^t{\mathrm{\ϵ}}_R\left(t\right)dt\\ \mathrm{\ϵ}\left(t\right)=-\frac{2C_o}{L}{\mathrm{\ϵ}}_R\left(t\right)\end{array}\right.---\left(8\right)$

In formula (8): E is the elastic modelling quantity of bar material, A and A_sIt is respectively bar and the cross-sectional area of test specimen, C₀For stress wave in bar Spread speed, L is specimen length；

Utilize method of least square to be fitted processing yield stress strain, obtain the value of C in formula (3)；

4th step, carries out tension test to test specimen on high temperature quasi-static test platform, it is thus achieved that curves of stress-strain relationship； Utilize method of least square that yield strength at each temperature is fitted, obtain the value of m in formula (4)；

From first to the 4th, step has obtained the extensograph parameter value of Johnson-Cook constitutive model；

5th step, carries out quasistatic and dynamic compressive test to alusil alloy ADC12 material under normal temperature condition, draws relevant answering Power-strain curve；From curves of stress-strain relationship, obtain the yield strength under each strain rate, obtain quasistatic compression Under the conditions of the yield strength i.e. value of A, utilize method of least square alignment static compression test data be fitted obtaining matching As a result, the value of B and n in strain hardening item is obtained accordingly；

6th step, is fitted dynamic compressive test result method of least square, obtains the value of C in strain rate hardening item；

The compression test parameter value of J-C constitutive model is obtained by the 5th step and the 6th step.