细化多轴疲劳（如拉扭复合）或织构定量分析（如 Schmid 因子分布）

细化多轴疲劳（如拉扭复合）或织构定量分析（如Schmid因子分布）一、钛合金HCP多轴疲劳适配（拉扭复合加载）多轴疲劳核心是剪切/正应力耦合损伤

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不同滑移系的多轴激活，以下是α-Ti600℃拉扭复合疲劳的完整实现方案：1.多轴疲劳模型扩展（PROPS新增参数）PROPS序号参数名物理意义示例值（α-Ti）25tau_c0_pyramid锥面滑移初始临界分切应力（MPa）100.026h_ii_pyramid锥面自硬化系数700.027beta_shear剪切应力损伤权重1.528beta_normal正应力损伤权重0.529multiaxial_fac多轴应力修正系数1.22.多轴滑移系激活（新增锥面滑移{10-11}<11-20>）fortran!修正滑移系数量（基面6+柱面6+锥面12=24个）INTEGER,PARAMETER::NSYSTEM=24!步骤4升级：初始化HCP全滑移系施密特矩阵（基面+柱面+锥面）SUBROUTINEINIT_SCHMID_HCP_FULL(schmid,NS)INTEGER,INTENT(IN)::NSREAL*8,INTENT(OUT)::schmid(NS,6)REAL*8::c_a=1.586D0,sqrt3=SQRT(3.0D0),sqrt6=SQRT(6.0D0)INTEGER::i,alpha!1.基面{0001}<11-20>（1-6）DOi=1,6alpha=ischmid(alpha,1)=(1.0D0/3.0D0)*MERGE(1.0D0,-1.0D0,MOD(i,2)==1)schmid(alpha,2)=(1.0D0/3.0D0)*MERGE(1.0D0,-1.0D0,MOD(i+1,2)==1)schmid(alpha,6)=(1.0D0/3.0D0)ENDDO!2.柱面{10-10}<11-20>（7-12）DOi=1,6alpha=i+6schmid(alpha,1)=(1.0D0/4.0D0)*MERGE(1.0D0,-1.0D0,MOD(i,2)==1)schmid(alpha,2)=(1.0D0/4.0D0)*MERGE(1.0D0,-1.0D0,MOD(i+1,2)==1)schmid(alpha,4)=(1.0D0/4.0D0)ENDDO!3.锥面{10-11}<11-20>（13-24）DOi=1,12alpha=i+12schmid(alpha,1)=(1.0D0/sqrt6)*MERGE(1.0D0,-1.0D0,MOD(i,2)==1)schmid(alpha,2)=(1.0D0/sqrt6)*MERGE(1.0D0,-1.0D0,MOD(i+1,2)==1)schmid(alpha,5)=(1.0D0/sqrt6)ENDDOENDSUBROUTINEINIT_SCHMID_HCP_FULL3.多轴应力耦合损伤模型fortran!步骤8升级：多轴应力损伤演化REAL*8::sigma_normal(3),tau_shear(3),damage_shear,damage_normalREAL*8::eqv_stress!多轴等效应力!提取正应力和剪切应力（Voigt形式）sigma_normal=[STRESS(1),STRESS(2),STRESS(3)]!σ11,σ22,σ33tau_shear=[STRESS(4),STRESS(5),STRESS(6)]!σ23,σ13,σ12!计算剪切/正应力损伤damage_shear=PROPS(27)*SUM(ABS(tau_shear))*cycle_num*PROPS(21)damage_normal=PROPS(28)*SUM(ABS(sigma_normal))*cycle_num*PROPS(21)!多轴等效应力修正eqv_stress=(SUM(sigma_normal**2)+3*SUM(tau_shear**2))**0.5D=D+(damage_shear+damage_normal)*PROPS(29)*(eqv_stress/200.0D0)!不同滑移系损伤权重（锥面滑移对剪切应力更敏感）DOalpha=1,NSYSTEMIF(alpha.GE.13)THEN!锥面滑移系D_alpha(alpha)=D_alpha(alpha)*1.8!增大损伤权重ELSEIF(alpha.GE.7)THEN!柱面滑移系D_alpha(alpha)=D_alpha(alpha)*1.2ENDIFENDDOD=MIN(D+MAXVAL(D_alpha),1.0D0)二、织构定量分析（Schmid因子分布+EBSD定量对比）1.Schmid因子分布提取（UMAT扩展输出）fortran!步骤5后添加：计算并存储Schmid因子（SDV42-65）REAL*8::schmid_factor(NSYSTEM)DOalpha=1,NSYSTEMschmid_factor(alpha)=DOT_PRODUCT(schmid(alpha,:),STRESS(1:6))/MAXVAL(ABS(STRESS))STATEV(41+alpha)=schmid_factor(alpha)!SDV42-65存储各滑移系Schmid因子ENDDO!输出Schmid因子统计信息（调试用）IF(MOD(KINC,100)==0)THENWRITE(*,*)'Grain',NOEL,'MaxSchmidFactor=',MAXVAL(schmid_factor)WRITE(*,*)'BasalSchmidFactor=',AVG(schmid_factor(1:6))ENDIF2.MTEX定量对比EBSD织构（1）提取Abaqus织构数据导出欧拉角+Schmid因子数据：python运行#AbaqusPython脚本（提取ODF数据）fromabaqusimport*fromabaqusConstantsimport*importodbAccessodb=odbAccess.openOdb('ti_hcp_fatigue.odb')frame=odb.steps['Step-1'].frames[-1]#最后一个循环帧euler_field=frame.fieldOutputs['SDV39']#φ1Phi_field=frame.fieldOutputs['SDV40']#Φphi2_field=frame.fieldOutputs['SDV41']#φ2#写入txt文件withopen('texture_data.txt','w')asf:foreuler,Phi,phi2inzip(euler_field.values,Phi_field.values,phi2_field.values):f.write(f'{euler.data}{Phi.data}{phi2.data}\n')（2）MTEX定量分析代码matlab%1.导入Abaqus和EBSD数据cs=crystalSymmetry('6/mmm',[2.954.68],'mineral','Ti');abaqus_euler=load('texture_data.txt');ebsd_euler=load('ebsd_texture.txt');%EBSD实验欧拉角%2.计算ODF并定量对比odf_abaqus=calcODF(Euler(deg2rad(abaqus_euler)),cs);odf_ebsd=calcODF(Euler(deg2rad(ebsd_euler)),cs);%3.织构强度定量指标%（1）最大织构强度max_int_abaqus=max(odf_abaqus(:));max_int_ebsd=max(odf_ebsd(:));fprintf('Abaqus织构强度：%.2f，EBSD织构强度：%.2f\n',max_int_abaqus,max_int_ebsd);%（2）Schmid因子分布对比schmid_abaqus=load('schmid_factor_abaqus.txt');schmid_ebsd=load('schmid_factor_ebsd.txt');%绘制分布直方图figure;subplot(1,2,1);histogram(schmid_abaqus,20);title('AbaqusSchmid因子分布');subplot(1,2,2);histogram(schmid_ebsd,20);title('EBSDSchmid因子分布');%（3）织构相似度（向量化对比）vec_abaqus=odf2vec(odf_abaqus);vec_ebsd=odf2vec(odf_ebsd);similarity=dot(vec_abaqus,vec_ebsd)/(norm(vec_abaqus)*norm(vec_ebsd));fprintf('织构相似度：%.2f\n',similarity);%越接近1，匹配度越高三、Abaqus/CAE多轴疲劳加载操作步骤步骤1：定义拉扭复合加载创建多轴分析步：同单轴疲劳，勾选“Coupledtemperature-displacement”；施加拉扭载荷：轴向（Z）：正弦波应力±200MPa（*Cload,AMPLITUDE=Axial_Amp）；扭转（XY平面）：剪切应力±50MPa（*Cload,AMPLITUDE=Torsion_Amp）；温度边界：恒定600℃（873K）。步骤2：输出多轴疲劳/织构变量编辑*Output,Field：勾选SDV1-65（滑移应变、损伤、欧拉角、Schmid因子）；勾选剪切应力（S6）、正应力（S3）；输出频率：每10个增量步（捕捉多轴循环特征）。步骤3：提交多轴疲劳作业bash运行abaqusjob=ti_hcp_multiaxial_fatigueinput=poly_ti.inpuser=umat_hcp_multiaxial.f90-fortlib=/opt/intel/mkl/lib/intel64-cpus=16四、完整UMAT核心模块（多轴疲劳+织构定量）fortran!UMATforHCPTimultiaxialfatigue+texturequantitativeanalysisINCLUDE'ABA_PARAM.INC'SUBROUTINEUMAT(STRESS,STATEV,DDSDDE,SSE,SPD,SCD,RPL,1DDSDDT,DRPLDE,DRPLDT,2STRAN,DSTRAN,TIME,DTIME,TEMP,DTEMP,PREDEF,DPRED,CMNAME,3NDI,NSHR,NTENS,NSTATV,PROPS,NPROPS,COORDS,DROT,PNEWDT,4CELENT,DFGRD0,DFGRD1,NOEL,NPT,LAYER,KSPT,JSTEP,KINC)!核心变量声明REAL*8,PARAMETER::PI=3.141592653589793D0INTEGER,PARAMETER::NSYSTEM=24!基面6+柱面6+锥面12REAL*8::C_elastic(6,6),schmid(NSYSTEM,6),tau(NSYSTEM),dot_gamma(NSYSTEM)REAL*8::tau_c(NSYSTEM),gamma(NSYSTEM),d_gamma(NSYSTEM),L_p(6,6),D_ep(6,6)REAL*8::gamma_rev(NSYSTEM),cycle_num,D,D_alpha(NSYSTEM),schmid_factor(NSYSTEM)REAL*8::sigma_normal(3),tau_shear(3),damage_shear,damage_normal,eqv_stressREAL*8::Rot(3,3),Rot_new(3,3),phi1,Phi,phi2,omega(3)INTEGER::i,j,alpha!步骤1：读取参数T_ref=298.0D0R=8.314D0T_current=TEMP!步骤2：初始化状态变量（扩展至SDV65）IF(KINC.EQ.1.AND.JSTEP.EQ.1)THEN!滑移应变/临界分切应力/反向滑移应变DOalpha=1,NSYSTEMSTATEV(alpha)=0.0D0!基面/柱面/锥面初始tau_cIF(alpha.LE.6)THENSTATEV(alpha+NSYSTEM)=PROPS(9)ELSEIF(alpha.LE.12)THENSTATEV(alpha+NSYSTEM)=PROPS(10)ELSESTATEV(alpha+NSYSTEM)=PROPS(25)ENDIFSTATEV(alpha+2*NSYSTEM)=0.0D0!gamma_revSTATEV(41+alpha)=0.0D0!Schmid因子ENDDOSTATEV(37)=0.0D0!循环次数STATEV(38)=0.0D0!损伤值STATEV(39:41)=[PROPS(22),PROPS(23),PROPS(24)]!欧拉角STATEV(40)=0.0D0!应力方向标记ENDIF!步骤3：读取状态变量cycle_num=STATEV(37)D=STATEV(38)phi1=STATEV(39)*PI/180.0D0Phi=STATEV(40)*PI/180.0D0phi2=STATEV(41)*PI/180.0D0DOalpha=1,NSYSTEMgamma(alpha)=STATEV(alpha)tau_c(alpha)=STATEV(alpha+NSYSTEM)gamma_rev(alpha)=STATEV(alpha+2*NSYSTEM)ENDDO!步骤4：构建弹性刚度矩阵（损伤退化）CALLBUILD_C_ELASTIC_HCP(PROPS,C_elastic)IF(D>=PROPS(20))C_elastic=C_elastic*(1.0D0-D)!步骤5：初始化全滑移系施密特矩阵（取向旋转）CALLINIT_SCHMID_HCP_FULL(schmid,NSYSTEM)CALLEULER2ROT(phi1,Phi,phi2,Rot)schmid=MATMUL(schmid,Rot)!步骤6：计算分切应力+Schmid因子DOalpha=1,NSYSTEMtau(alpha)=DOT_PRODUCT(schmid(alpha,:),STRESS(1:6))schmid_factor(alpha)=tau(alpha)/MAXVAL(ABS(STRESS))STATEV(41+alpha)=schmid_factor(alpha)!存储Schmid因子ENDDO!步骤7：剪切应变率（幂律模型）DOalpha=1,NSYSTEMdot_gamma(alpha)=MERGE(0.0D0,PROPS(7)*(ABS(tau(alpha)/tau_c(alpha))**(1.0D0/PROPS(8)))*SIGN(1.0D0,tau(alpha)),ABS(tau_c(alpha))<1e-6)d_gamma(alpha)=dot_gamma(alpha)*DTIMEENDDO!步骤8：多轴循环硬化（温度依赖）DOalpha=1,NSYSTEMgamma_amplitude=ABS(gamma(alpha)-gamma_rev(alpha))!基面/柱面/锥面分别硬化IF(alpha.LE.6)THENh_base=PROPS(11)+PROPS(18)*cycle_num/PROPS(19)tau_cs=PROPS(14)*EXP(-PROPS(16)*1000.0D0/(R*T_current)+PROPS(16)*1000.0D0/(R*T_ref))tau_c(alpha)=tau_cs-(tau_cs-PROPS(9))*EXP(-h_base*gamma(alpha))ELSEIF(alpha.LE.12)THENh_prism=PROPS(12)+PROPS(18)*cycle_num/PROPS(19)tau_cs=PROPS(15)*EXP(-PROPS(17)*1000.0D0/(R*T_current)+PROPS(17)*1000.0D0/(R*T_ref))tau_c(alpha)=tau_cs-(tau_cs-PROPS(10))*EXP(-h_prism*gamma(alpha))ELSEh_pyramid=PROPS(26)+PROPS(18)*cycle_num/PROPS(19)tau_cs=PROPS(14)*1.5D0*EXP(-PROPS(16)*1000.0D0/(R*T_current)+PROPS(16)*1000.0D0/(R*T_ref))tau_c(alpha)=tau_cs-(tau_cs-PROPS(25))*EXP(-h_pyramid*gamma(alpha))ENDIF!反向滑移更新IF(SIGN(1.0D0,tau(alpha))/=SIGN(1.0D0,gamma(alpha)))THENgamma_rev(alpha)=gamma(alpha)ENDIFENDDO!步骤9：多轴耦合损伤演化sigma_normal=[STRESS(1),STRESS(2),STRESS(3)]tau_shear=[STRESS(4),STRESS(5),STRESS(6)]damage_shear=PROPS(27)*SUM(ABS(tau_shear))*cycle_num*PROPS(21)damage_normal=PROPS(28)*SUM(ABS(sigma_normal))*cycle_num*PROPS(21)eqv_stress=(SUM(sigma_normal**2)+3*SUM(tau_shear**2))**0.5!不同滑移系损伤权重DOalpha=1,NSYSTEMIF(alpha.LE.6)THEND_alpha(alpha)=(damage_shear+damage_normal)*1.0ELSEIF(alpha.LE.12)THEND_alpha(alpha)=(damage_shear+damage_normal)*1.2ELSED_alpha(alpha)=(damage_shear+damage_normal)*1.8ENDIFENDDOD=D+MAXVAL(D_alpha)*PROPS(29)*(eqv_stress/200.0D0)D=MIN(D,1.0D0)!步骤10：塑性本构矩阵+弹塑性刚度L_p=0.0D0DOalpha=1,NSYSTEMIF(ABS(tau_c(alpha))>1e-6)THENDOi=1,6DOj=1,6L_p(i,j)=L_p(i,j)+schmid(alpha,i)*schmid(alpha,j)*dot_gamma(alpha)/tau_c(alpha)ENDDOENDDOENDIFENDDOCALLINV_MATRIX_6X6(C_elastic,C_elastic_inv)D_ep=C_elastic_inv+L_pCALLINV_MATRIX_6X6(D_ep,DDSDDE)!步骤11：更新应力DOi=1,6STRESS(i)=STRESS(i)+MATMUL(DDSDDE(i,:),DSTRAN(1:6))ENDDO!步骤12：取向旋转更新（多轴滑移驱动）CALLEULER2ROT(phi1,Phi,phi2,Rot)!多轴滑移驱动旋转（基面+锥面主导）omega(1)=SUM(d_gamma(1:6))*5e-4!X轴旋转omega(2)=SUM(d_gamma(13:24))*3e-4!Y轴旋转omega(3)=SUM(d_gamma(7:12))*1e-3!Z轴旋转!旋转矩阵更新（三轴旋转）Rot_new=Rot*[COS(omega(1)*DTIME),-SIN(omega(1)*DTIME),0.0D0,SIN(omega(1)*DTIME),COS(omega(1)*DTIME),0.0D0,0.0D0,0.0D0,1.0D0]Rot_new=Rot_new*[COS(omega(2)*DTIME),0.0D0,SIN(omega(2)*DTIME),0.0D0,1.0D0,0.0D0,-SIN(omega(2)*DTIME),0.0D0,COS(omega(2)*DTIME)]Rot_new=Rot_new*[1.0D0,0.0D0,0