development of material model for crack propagation of

6. LS-DYNA Anwenderforum, Frankenthal 2007

© 2007 Copyright by DYNAmore GmbH

Development of Material Model for

Crack Propagation of Casted Aluminum

Author

Hiroki Yamasaki1, Ritsu Nishimura

2 1 TOYOTA MOTOR CORPORATION, Japan 2TOYOTA TECHNICAL DEVELOPMENT CORPORATION, Japan

Summary:

This paper describes development of a material model for simulationg crack propagation of casted Aluminum parts. Authors established a new method for predicting the local fracture strain and strength dependent on solidification time during casting. Also, we introduced another new material model for estimating crack propagation with bi-axial stress distribution. These method and model were applied to a test piece simulation of Aluminum casted parts subject to tensile loads. The crack propagation by FE analysis showed good correlation with that of test. Also, Aluminum sub frame compression test was performedand the crack propagation and force-displacement charcteristics showed a good correlation with that of test. Keywords:

Computer Aided Engineering(CAE) ,FEM, Modeling, Crashworthiness /Aluminum ,Material

Crash II - Schadensmodellierung

B - II - 1



1 INTRODUCTION

In recent years, Aluminum has been replaced with steel as non-ferrous material for the purpose of lightening of a vehicle and is widely applied to exterior panels and frame structures[1]. Fracture strain of Aluminum is less than steel and an exclusive productive method such as extrusions and casting is available besides panels as a vehicle body structures. Therefore, the modeling technique specialized to Aluminum for the simulation of fracture becomes more necessary in addition to the crash CAE technology which has been mainly focused on steel. Technical development which were implemented so far, as follows.

(1)modeling technique of the thick part of extrusion for crash-box [2] (2)modeling technique of the arc welding part[3] (3)prediction of the fracture of a casted B-pillar in the case of a side collision[4]

The damage fracture material model (hereafter, the damage fracture material model is reffered as to The conventional model) is used in the fracture prediction of the B-pillar . Meanwhile, the Aluminum casted parts such as B-pillar and sub-frame and so on, it is well-known that the material properties of each part depend on the solidification time during casting[5]. If a physical casted part is available and the measurement of the material properties partially could be done, the computational simulation showed better prediction by taking into acount of distributions of yielding stress and so on. However, in the designing step which the physical casted part is not available, it is difficult to consider the distribution of the material properties, because of the lack of measured distributions of yielding stress and so on.

Also, in the case of bending deformation of the B-pillar under the side collision , the conventional material model had enough precision to predict fracture. However, in the case of multiple input-condition of bending and compression of the sub-frame under the front crash collision , the conventional material model did not have enough precision to predict fracture. Therefore,it is necessary to predict more precisely the crack initiation and propagation than the conventional material model .

This paper presents the development of the material model for casted aluminum based on the characteristics discussed above. Then the validation is carried out and the results show the good agreement with the test data.

2 Precision of conventional model

By using the conventional model, the verification of sub-frame under a static compression was executed and the results shows, (1) The crack initiation and propagation positions are different from the test results, (2)force-displacement characteristics is diffrent from the test(Figure 1 and 2). It is thought that the prediction of deformation of the frame in the practical vehicle was difficult due to the insufficient accuracy of the prediction of crack propagation.

Fig.1 Crack propagation of Sub-frame Fig.2 Force-displacement curve of Sub-frame

The authors assumed following hypotheses for the difference of the above-mentioned. (1)Difference in crack position Hypothesis 1: The distribution of the material property that originates due to the difference of the

solidification time of each part might influence. (2)Difference of force-displacement characteristics Hypothesis 2: The rupture order difference might influence the whole progress of the crack

development.

Not correlation with Test

CAE Test

DisplacementForce DisplacementForce DisplacementForce DisplacementForce Test CAE



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Based on the above-mentioned hypotheses, the following measures are planned. Measures 1: the distribution of the material property by using the casted analysis result (hereafter,

call it model with material properties distribution consideration). Measures 2: The Wilkins model for the crack progergation(hereafter, Wilkins model) is adopted. That is, a method combining and two models: " model with material properties distribution

consideration " and "Wilkins model" is developed.

3 Consideration of material property distribution of Aluminum parts

An original technique (Figure 3) for the material property distribution consideration is developed. First of all, the correlation of the solidification time of existing aluminum parts ((1) in Figure 3) and the material property ((2) in Figure 3)((3) in Figure 3) is taken in STEP1. Next, STEP2, the distribution of the material property is presumed by using the correlation formula ((3) in Figure 3) obtained from the solidification time distribution ((4) in Figure 3) output by the casted simulations of the parts in STEP1, and then converted into a material data ((5) and (6) in Figure 3) for Crash CAE (Hereafter, it is called the mapping).

Fig.3 Definition of material properties The details are described as follows.

3.1 Making of correlation formula of solidification time and material properties

When the casted Aluminum parts manufactured, the solidification time is different from thier local position. Then, the solidification time of about 20 different positions has been extracted from the casted simulation results of existing parts. In addition, the material properties are measured for the test pieces cut out at the positions(Figure 4).

The elongation, from the beginning till the necking point, was recorded with the video recorder which is used to obtain true stress-true strain diagram, and data is measured from the images.

Translation

CastCastCastCastCAECAECAECAECastCastCastCastCAECAECAECAE MappingMappingMappingMappingProgramProgramProgramProgram

σ εσ εSTEP1

STEP2

Crash Crash Crash Crash CAECAECAECAECrash Crash Crash Crash CAECAECAECAEσ εσs 　tsd１ εf 　tsd１ σy 　tsd１σs 　tsd１σs 　tsd１ εf 　tsd１εf 　tsd１ σy 　tsd１σy 　tsd１Translation

CastCastCastCastCAECAECAECAECastCastCastCastCAECAECAECAECastCastCastCastCAECAECAECAECastCastCastCastCAECAECAECAE MappingMappingMappingMappingProgramProgramProgramProgramMappingMappingMappingMappingProgramProgramProgramProgram

σ εσ εσ εσ εSTEP1

STEP2

Crash Crash Crash Crash CAECAECAECAECrash Crash Crash Crash CAECAECAECAEσ εσ εσs 　tsd１ εf 　tsd１ σy 　tsd１σs 　tsd１σs 　tsd１ εf 　tsd１εf 　tsd１ σy 　tsd１σy 　tsd１σs 　tsd１σs 　tsd１ εf 　tsd１εf 　tsd１ σy 　tsd１σy 　tsd１σs 　tsd１σs 　tsd１ εf 　tsd１εf 　tsd１ σy 　tsd１σy 　tsd１

< Physical Casted Part >

< Casted part of designing >

Correlation function ・Strength σs＝fun(Solidification time) ・Fracture strain εｆ＝fun(solidification time) ・Yield Stress σｙ＝fun(Solidification time)

Distribution of solidification time

By using correlation, translating Cast CAE solidification time data into Crash CAE input data

Distribution of mechanical properties

Measurement of mechanical properties of Aluminum casted part

Coupon test data

Distribution of solidification time

(1)

(2)

(4)

(5) (6)

(3)


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Fig.4 Measurement of material properties

The material properties such as tensile strength, the rupture strain, and yield strength, etc. are extracted from the stress-strain diagram of the test result, and the correlation formula of each properties was decided from the correlation with the solidification time that had been calculated beforehand by the casted simulation. Figure 5 shows the detail correlation formula made from the data of the object of Hat-section shaped specimen and B pillar.

Fig.5 Correlation between properties and solidification time

3.2 Estimation of material property distribution based on solidification time

The casting simulation of a sub-frame was performed, and the distribution of solidification time was obtained. The data is converted into the material property by using the above-mentioned correlation formula, and, in addition, it is converted into material data and input data format for collision CAE (Figure 6).

The mapping algorithm is described in the next paragraph. Fig.6 Mapping to input data for crash analysis

3.3 Mapping algorithm

The stress-strain properties is expressed by overlapping the damage function with the undamage properties (compression properties) of the material model used for aluminum so far (Figure 7) [6].

InputInputInputInput DataDataDataData forforforfor CrashCrashCrashCrash AnalysisAnalysisAnalysisAnalysis CastedCastedCastedCasted SimulationSimulationSimulationSimulation long

short

MappingMappingMappingMapping ProgramProgramProgramProgram

InputInputInputInput DataDataDataData forforforfor CrashCrashCrashCrash AnalysisAnalysisAnalysisAnalysis CastedCastedCastedCasted SimulationSimulationSimulationSimulation long

short

MappingMappingMappingMapping ProgramProgramProgramProgram

(a) (b)

Strength = A ln(Solidification time) + B

A,B=constant Fracture Strain = C ln(Solidification time) + D

C,D=constant Distribution of solidification time

Distribution of mechanical properties

－＝ εεεεFFFFDamage propertyDamage propertyDamage propertyDamage property

ε Fracture StrainFracture StrainFracture StrainFracture StrainFailure beginsFailure beginsFailure beginsFailure beginsStress Stress Stress Stress ---- Strain propertyStrain propertyStrain propertyStrain propertySSSSｔｒｅｓｓｔｒｅｓｓｔｒｅｓｓｔｒｅｓｓσσσσ Strain Strain Strain Strain εεεε SSSSｔｒｅｓｓｔｒｅｓｓｔｒｅｓｓｔｒｅｓｓσσσσ SSSSｔｒｅｓｓｔｒｅｓｓｔｒｅｓｓｔｒｅｓｓσσσσ Strain Strain Strain Strain εεεε－＝ εεεεFFFFεεεεFFFF

Damage propertyDamage propertyDamage propertyDamage propertyε Fracture StrainFracture StrainFracture StrainFracture StrainFailure beginsFailure beginsFailure beginsFailure begins

Stress Stress Stress Stress ---- Strain propertyStrain propertyStrain propertyStrain propertySSSSｔｒｅｓｓｔｒｅｓｓｔｒｅｓｓｔｒｅｓｓσσσσ Strain Strain Strain Strain εεεε SSSSｔｒｅｓｓｔｒｅｓｓｔｒｅｓｓｔｒｅｓｓσσσσ SSSSｔｒｅｓｓｔｒｅｓｓｔｒｅｓｓｔｒｅｓｓσσσσ Strain Strain Strain Strain εεεε

Coupon

Stress – Strain Curve (Coupon Test Result)

Solidification Simulation Stress Strain Stress Strain

引張り強さ = -45.199 ln（凝固時間） + 286.16相関係数 = 0.7036050100150200250300350-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8ln(凝固時間)引張り強さ(MPa) グループごとの平均値相関式破断ひずみ = -1.5829 ln（凝固時間） + 8.3835相関係数 = 0.6001051015

20-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8ln(凝固時間)破断ひずみ(%) グループごとの平均値相関式引張り強さ = -45.199 ln（凝固時間） + 286.16相関係数 = 0.7036050100150200250300350

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8ln(凝固時間)引張り強さ(MPa) グループごとの平均値相関式引張り強さ = -45.199 ln（凝固時間） + 286.16相関係数 = 0.7036050100150200250300350-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8ln(凝固時間)引張り強さ(MPa) グループごとの平均値相関式破断ひずみ = -1.5829 ln（凝固時間） + 8.3835相関係数 = 0.6001051015

20-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8ln(凝固時間)破断ひずみ(%) グループごとの平均値相関式破断ひずみ = -1.5829 ln（凝固時間） + 8.3835相関係数 = 0.6001051015

20-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8ln(凝固時間)破断ひずみ(%) グループごとの平均値相関式Fracture Strain

= C ln(Solidification time) + D

C,D=constant

Fracture Strainln(Solidification time)ln(Solidification time)ln(Solidification time)ln(Solidification time) Strength Strength

= A ln(Solidification time) + B

A,B=constant ln(Solidification time)ln(Solidification time)ln(Solidification time)ln(Solidification time) Fra

ctu

re S

train

Str

ength StrengthStrengthStrengthStrength Fracture StrainFracture StrainFracture StrainFracture Strain

Fig.7 Material model


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Then, a standard undamage property was common and damage property was varied with solidification time by using the correlation formula mentioned above. The procedure is described as follows. First of all, the value of the solidification time and the material property is decided from each correlation formula (Figure 8).

Fig.8 Determination of properties from correlation

Next, a standard undamage property (compression property) is decided from the maximum tensile strength of test data stress-strain properties (Figure 9).

Fig.9 Determination of base undamage curve

Next, the scale factors correlation was made from the ratio of the standard undamage curve to the tested curve of tensile strength, as showed in Figure 10.

Finally, the stress-strain properties corresponding to each solidification time can be obtained by

overlapping the damage properties, which are obtained by multiplying the undamage curve with the scale factor and the rupture strain,respectively (Figure 11).

UndamageUndamageUndamageUndamage propertypropertypropertypropertyand Sand Sand Sand S----S curveS curveS curveS curve １S3 σs１σs2σs3σs4S1S2 StrengthStrengthStrengthStrengthS = fun(Strength)S = fun(Strength)S = fun(Strength)S = fun(Strength)Ｓｃａｌｅ　Ｓｃａｌｅ　Ｓｃａｌｅ　Ｓｃａｌｅ　factorfactorfactorfactor　　　　SSSSσs4σs1σs2σs3 Base SBase SBase SBase S----SSSScurvecurvecurvecurveCalculating Calculating Calculating Calculating of damageof damageof damageof damageStrain Strain Strain Strain εεεεSSSSｔｒｅｓｓｔｒｅｓｓｔｒｅｓｓｔｒｅｓｓσσσσ １１１１ S3

S2S1

Base damageBase damageBase damageBase damagecurvecurvecurvecurveDamage propertyDamage propertyDamage propertyDamage propertySSSSｔｒｅｓｓｔｒｅｓｓｔｒｅｓｓｔｒｅｓｓσσσσ Strain Strain Strain Strain εεεε

UndamageUndamageUndamageUndamage propertypropertypropertypropertyand Sand Sand Sand S----S curveS curveS curveS curve １S3 σs１σs2σs3σs4S1S2 StrengthStrengthStrengthStrengthS = fun(Strength)S = fun(Strength)S = fun(Strength)S = fun(Strength)Ｓｃａｌｅ　Ｓｃａｌｅ　Ｓｃａｌｅ　Ｓｃａｌｅ　factorfactorfactorfactor　　　　SSSS１S3S3 σs１σs１σs2σs2σs3σs3σs4σs4S1S1S2S2 StrengthStrengthStrengthStrengthS = fun(Strength)S = fun(Strength)S = fun(Strength)S = fun(Strength)Ｓｃａｌｅ　Ｓｃａｌｅ　Ｓｃａｌｅ　Ｓｃａｌｅ　factorfactorfactorfactor　　　　SSSSσs4σs4σs1σs1σs2σs2σs3σs3 Base SBase SBase SBase S----SSSScurvecurvecurvecurveCalculating Calculating Calculating Calculating of damageof damageof damageof damageStrain Strain Strain Strain εεεεSSSSｔｒｅｓｓｔｒｅｓｓｔｒｅｓｓｔｒｅｓｓσσσσ １１１１ S3

S2S1

Base damageBase damageBase damageBase damagecurvecurvecurvecurveDamage propertyDamage propertyDamage propertyDamage propertySSSSｔｒｅｓｓｔｒｅｓｓｔｒｅｓｓｔｒｅｓｓσσσσ Strain Strain Strain Strain εεεε

－＝

Base Base Base Base undamage undamage undamage undamage curvecurvecurvecurveCommon

undamage

curve

Change the

damage　

property

1

Base Base Base Base damagedamagedamagedamagecurvecurvecurvecurve Stress - Strain curveεChange with the fracture strain

Change withChange withChange withChange withthe scale the scale the scale the scale factorfactorfactorfactorSSSSｔｒｅｓｓｔｒｅｓｓｔｒｅｓｓｔｒｅｓｓσσσσ Strain Strain Strain Strain εεεε Strain Strain Strain Strain εεεε Strain Strain Strain Strain εεεεSSSSｔｒｅｓｓｔｒｅｓｓｔｒｅｓｓｔｒｅｓｓσσσσ SSSSｔｒｅｓｓｔｒｅｓｓｔｒｅｓｓｔｒｅｓｓσσσσ－＝

Base Base Base Base undamage undamage undamage undamage curvecurvecurvecurveBase Base Base Base undamage undamage undamage undamage curvecurvecurvecurveCommon

undamage

curve

Change the

damage　

property

1

Base Base Base Base damagedamagedamagedamagecurvecurvecurvecurve1

Base Base Base Base damagedamagedamagedamagecurvecurvecurvecurve Stress - Strain curveεεChange with the fracture strain

Change withChange withChange withChange withthe scale the scale the scale the scale factorfactorfactorfactorSSSSｔｒｅｓｓｔｒｅｓｓｔｒｅｓｓｔｒｅｓｓσσσσ Strain Strain Strain Strain εεεε Strain Strain Strain Strain εεεε Strain Strain Strain Strain εεεεSSSSｔｒｅｓｓｔｒｅｓｓｔｒｅｓｓｔｒｅｓｓσσσσ SSSSｔｒｅｓｓｔｒｅｓｓｔｒｅｓｓｔｒｅｓｓσσσσ

BaseBaseBaseBaseundamageundamageundamageundamagecurvecurvecurvecurveStrain Strain Strain Strain εεεεSSSSｔｒｅｓｓｔｒｅｓｓｔｒｅｓｓｔｒｅｓｓσσσσ Strain Strain Strain Strain εεεεSSSSｔｒｅｓｓｔｒｅｓｓｔｒｅｓｓｔｒｅｓｓσσσσ BaseBaseBaseBaseundamageundamageundamageundamagecurvecurvecurvecurveStrain Strain Strain Strain εεεεSSSSｔｒｅｓｓｔｒｅｓｓｔｒｅｓｓｔｒｅｓｓσσσσ Strain Strain Strain Strain εεεεSSSSｔｒｅｓｓｔｒｅｓｓｔｒｅｓｓｔｒｅｓｓσσσσｔsd1Solidification time ｔsdｔsd1Solidification time ｔsdσσσσs1s1s1s1 εf1StrengthStrengthStrengthStrengthσσσσssss FractureFractureFractureFracture　　　　StrainStrainStrainStrain　　　　εεεε

ｆｆｆｆｔsd1Solidification time ｔsdｔsd1Solidification time ｔsdσσσσs1s1s1s1 εf1StrengthStrengthStrengthStrengthσσσσssss FractureFractureFractureFracture　　　　StrainStrainStrainStrain　　　　εεεε

ｆｆｆｆ

Fig.11 Determination of Stress-strain curve

Fig.10 Correlation between Strength and damage


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4 Method for simulating crack propagation

To simulate the propagation of the crack, the Wilkins model is used. This material model is the one in which rupture criteria [7][8] by Wilkins damage D shown in expression (1) was combined with the material model used for the aluminum so far.

pdD εωω 21∫= ・・・ (1)

Here, the ω1 is weight coefficient of hydrostatic pressure, ω2 is the weight coefficient of the

asymmetric component, and εp is the equivalent plastic strain. The Wilkins damage, based on the

ductility destruction theory proposed by McClintock, that the rupture occurs due to the damage that depends on the strain. As showed in Figure 12, the crack occurs when (1) Wilkins damage D reaches limit damage Dc, (2)the crack propagation is expressed by the change in stress scale F, and (3)the rupture occurs when stress scale F reaches one. An accurate crack forecast is possible for the biaxial stress state because in Wilkins damage model, the rupture judgment depends on the state of the stress which changes through out the process.

5 Verification of test

Using the crack propagation material model proposed above, the new aluminum models(hereafter, call it new model) were made for those objects. The comparison of the model specifications with conventional material models (call it hereafter conventional model) is shown in table 1. No tuning of material property in the model was done, and a uniform material property was used.

The verification is done for this model, and in addition, the verification is also done for sub-frame, which receives a static compression load.

Table.1 Comparison of FE model specification

5.1 Verification of test pieces

Test pieces with various shapes under different tension and bending loads, about 10 cases were verified. Excellent correspondence was obtained by all cases. Here, Table 2 reports the results of the typical 2 cases.

Table.2 Purpose of the validations

Conventional CAE CAE with New

model

Material model Elastic-plastic material model

Wilkins model

Material property distribution of casted

Not considered Considered

Purpose

Force-displacement

property

Crack initiation point

Crack propagation

Case1 Bending test of

T-section shaped specimen

― ― ○

Case2 Bending test of

Hat-section shaped specimen

○ ○ ―

Fig.12 Diagram of fracture propagation material model

Initial critical damage

Wilkins damage D (Change with the stress state )

strain (1)Crack initiation

(3)Fracture

Critical damage D

(2)Crack propagation

1Fracture fraction F

Elastic-plastic material curve stressStress stress


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5.1.1 verifications #1(T-section shaped specimen under three points bending moment)

T-section shaped specimen under three point bending test was performed on the condition, shows in Figure 13, that the rib is layed up wards with the forced displacement at the center part. The force-displacement diagram and deformation are shown in Figure 14 and Figure 15 respectively. It is noted, the rupture timing(A) predicted with the conventional model is earlier than the test data, while the results, like rupture timing (B)and force-displacement curve, predicted with new material model, are very close to the test data. Since the stress concentration of the T-section shaped specimen is a biaxial stress state in nature, and a new model is more accurate for the biaxial stress state.

5.1.2 Verifications #2(Hat-section shaped specimen under three points bending moment)

The Hat-section shaped specimen under three point bending test was executed, as showed in Figure 16, on the condition of giving a compulsive displacement to the center part of the Hat-section shaped specimen . The calculated displacement and force-displacement curve are shown in Figure 17 and Figure 18 respectively. Compare with the conventional model, the force-displacement curve, as well as the rupture situation predicted with the new model roughly agreed to the test, while maximum force predicted with the conventional model is high, and no rupture occurs surround the pin.

Because there is a difference in the thickness distribution in the test pieces, and the solidification time is different as shown in the solidification analysis result of Figure 19, the material property is not uniform. In addition, compare with other region, the rupture strain is much smaller around the pin area due to the slower solidification around the pin area. It is thought that the accuracy of the predicted displacement and force-displacement curve can be improved by considering the distribution of the material property, which is typical for such casted process, in the new model.

Displacement A Displacement B

Test

CAE with New model

Conventional CAE

Already fractured Bi-axial state Uni-axial state

DisplacementForceForce DisplacementA B

Test CAE with New model Conventional CAE

Fig.13 FE model of T-section shaped specimen

Fig.14 Force-displacement curve of T-section shaped specimen

Fig.15 Deformation and Stress state of T-shape specimen

Good correlation with Test


Bi-axial state

T-section shaped

specimen

300mmFixed


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5.2 Verification of sub-frame compression test

As showed in Figure 20, to obtain offset collision results, the sub-frame was set inclined up on the condition of giving the compulsion displacement to one of the connecting point with the vehicle. The force-displacement curve and the deformation are shown in Figure 21 and Figure 22 respectively. Compare with the tested data, the predicted maximum load is lower and the rupture region with the conventional model is different, while using new model the predicted results roughly agrees with the tested results. Especially, the new model improves the rupture prediction in region A, where rupture predicted as the test results, and this can not been seen with conventional model. As for this, the solidification of region A is early, and the rupture strain large and this effect has been taken into consideration in the new model. Moreover, the state of the stress and the rupture situation in the time series are compared with conventional model to investigate the rupture timing of the stress concentration region, as shown in Figure 23. The stress concentration part is a biaxial stress state, the same as T shaped specimen under three point bending test, and it confirmed that the rupture timing predicted with conventional model is earlier.

For purpose of investigating the rupture strain under biaxial stress state, 3 cases of biaxial tension calculation was performed. In conventional model, the maximum principal strain at rupture time keeps unchanged even while change the stress state. But with Wilkins models, the rupture strain changes accordingly. This can be explained as those Wilkins model responses well with the formation of boundary limit so that it can give a good accuracy in biaxial stress state. That's why it enhanced accuracy in predicting the rupture of sub-frame.

Hat-section shaped

specimen

Fixed 500mm DisplacementForceForce DisplacementDisplacementForceForce DisplacementTest CAE with New model Conventional CAE

Test



Conventional CAE CAE with New model A-A Section

Solidification Time

slow

fast

A

A

Fig.19 Solidification time distribution of Hat-section shaped specimen

Fig.18 Crack propagation of Hat-section shaped specimen

Fig.17 Force-displacement curve of Hat-section shaped specimen Fig.16 FE model of Hat-section shaped

specimen


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○○○○：Fixed

Sub-frame

6 Conclusions

The authors developed the method for casted Aluminum parts combining the Wilkins damage model and consideration of material property distribution. By using this method, the crack propagation and force-displacement characteristics were more accurately predicted. The verification confirmed that not only drawing information but also the material property distribution that originated from the solidification time in the manufacturing process are important factors in predicting the crack propagation.

DisplacementForce (a)

(b)

(c)

Test CAE w/New model Conventional CAE

Conventional CAE CAE with New model



A

Test

(c)

(c)

Conventional CAE

Earlier than

New model

(a)

(b)

(a)

(b)

Later than

Conventional

model

Stress

concentration

part

Stress

concentration

part

CAE with New model

Bi-axial

state

Uni-axial

state

Fig.20 FE model of Sub-frame Fig.21 Force-displacement curve of Sub-frame

Fig.23 Stress state and Crack condition of Sub-frame Fig.24 Bi-axial tensile simulation

Fig.22 Crack propagation of Sub-frame

Specimen

VX -VX

-VY

VY

V x VY

Case ◆ 1 ： 0

Case ■ 2 ： 1

Case ● 2 ： -1

■ ■

◆ ◆

● ●

Max principalstrain ε1Max principal strain is decreasing

Min principal strain ε2

Wilkins model

Elastic-plastic material model

Fracture strain is constant


B - II - 9



7 Literature [1]J.Christlein: The Audi Space Frame on the A2: A New Body Concept in Aluminum for Superior

Crashworthiness, ASME International Mechanical Engineering Congress and Exposition, p.33-41 (2001)

[2]Yuta Urushiyama, et al. :Resarch of Aluminum Crash Box for Crash Energy Absorbing, Honda R&D Technical Review Vol.13 No.2, p.141-148 (2001)

[3]A.G.Caliskan, R.Koganti: Frontal Impact Test & Analysis on an Aluminum Front-End Structure, ASME International Mechanical Engineering Congress and Exposition, p.111-117 (2001)

[4] T.Tsuchida, Y.Shibuya: The application of the damage & fracture material model to crashworthiness evaluations for Aluminum cars, SAE 2003-01-2776 (2003)

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development of material model for crack propagation of

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