疲勞加載（循環應力） 或織構演化分析

疲勞加載（循環應力）

或織構演化分析一、鈦合金HCP疲勞加載適配（600℃循環應力）疲勞模擬核心是循環硬化/軟化模型

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滑移系累積損傷演化，以下是針對α-Ti600℃低周疲勞（LCF）的完整適配方案：1.疲勞模型核心擴展（PROPS新增參數）PROPS序號參數名物理意義示例值（α-Ti）18h_cycle循環硬化/軟化系數-50.0（軟化）19N_fatigue疲勞壽命參考循環數100020D_critical臨界損傷值（失效閾值）0.821k_damage損傷演化系數1.0e-52.循環硬化/軟化模塊（替換單調硬化）fortran!步驟7升級：循環硬化+溫度依賴+飽和硬化REAL*8::gamma_rev(NSYSTEM)!反向滑移累積剪切應變（循環加載）REAL*8::cycle_num,gamma_amplitude!循環次數、滑移應變幅值!讀取循環相關狀態變量（SDV25-36：反向滑移應變；SDV37：循環次數；SDV38：損傷值）IF(KINC.EQ.1.AND.JSTEP.EQ.1)THENDOalpha=1,NSYSTEMSTATEV(alpha+24)=0.0D0!gamma_rev初始化ENDDOSTATEV(37)=0.0D0!循環次數初始化STATEV(38)=0.0D0!損傷值初始化ENDIFcycle_num=STATEV(37)DOalpha=1,NSYSTEMgamma_rev(alpha)=STATEV(alpha+24)ENDDO!識別循環加載方向（應力反向判斷）REAL*8::stress_amplitude=MAXVAL(STRESS)-MINVAL(STRESS)IF(stress_amplitude>1e-3.AND.SIGN(1.0D0,tau(1))/=SIGN(1.0D0,STATEV(40)))THENcycle_num=cycle_num+0.5D0!半循環計數STATEV(40)=tau(1)!記錄當前滑移應力方向ENDIF!循環硬化/軟化修正DOalpha=1,NSYSTEMgamma_amplitude=ABS(gamma(alpha)-gamma_rev(alpha))IF(alpha.LE.6)THEN!基面滑移系!循環軟化：h_cycle為負，隨循環次數降低硬化能力h_base=PROPS(11)+PROPS(18)*cycle_num/PROPS(19)tau_c(alpha)=tau_cs_base-(tau_cs_base-PROPS(9))*EXP(-h_base*gamma(alpha))ELSE!柱面滑移系h_prism=PROPS(12)+PROPS(18)*cycle_num/PROPS(19)tau_c(alpha)=tau_cs_prism-(tau_cs_prism-PROPS(10))*EXP(-h_prism*gamma(alpha))ENDIF!反向滑移應變更新（應力反向時記錄）IF(SIGN(1.0D0,tau(alpha))/=SIGN(1.0D0,gamma(alpha)))THENgamma_rev(alpha)=gamma(alpha)ENDIFENDDO3.滑移系累積損傷演化（基于Manson-Coffin）fortran!步驟8：損傷演化（SDV38為總損傷值）REAL*8::D,D_alpha(NSYSTEM)!總損傷、各滑移系損傷D=STATEV(38)D_alpha=0.0D0!各滑移系損傷：D_alpha=k_damage*gamma_amplitude^2*cycle_numDOalpha=1,NSYSTEMgamma_amplitude=ABS(gamma(alpha)-gamma_rev(alpha))D_alpha(alpha)=PROPS(21)*(gamma_amplitude**2)*cycle_numENDDO!總損傷（最大滑移系損傷主導）D=D+MAXVAL(D_alpha)!損傷閾值判斷（超過臨界值則剛度退化）IF(D>=PROPS(20))THEN!損傷失效：彈性剛度退化50%C_elastic=C_elastic*0.5D0!輸出失效信息WRITE(*,*)'Grain',NOEL,'failedatcycle',cycle_num,'Damage=',DENDIF!更新損傷狀態變量STATEV(38)=DSTATEV(37)=cycle_numDOalpha=1,NSYSTEMSTATEV(alpha+24)=gamma_rev(alpha)ENDDO二、織構演化分析（EBSD對比）織構演化核心是晶粒取向旋轉模型

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ODF（取向分布函數）提取，以下是Abaqus模擬與EBSD實驗對比的完整流程：1.取向旋轉模型（UMAT擴展）fortran!步驟11：晶粒取向旋轉（基于滑移系剪切應變）REAL*8::Rot(3,3),Rot_new(3,3),phi1,Phi,phi2!旋轉矩陣、歐拉角REAL*8::omega(3)!旋轉角速度（由滑移應變梯度驅動）!讀取當前歐拉角（SDV39-41：φ1,Φ,φ2）IF(KINC.EQ.1.AND.JSTEP.EQ.1)THEN!初始歐拉角（Neper導入值）STATEV(39)=PROPS(22)!φ1(deg)STATEV(40)=PROPS(23)!Φ(deg)STATEV(41)=PROPS(24)!φ2(deg)ENDIFphi1=STATEV(39)*PI/180.0D0Phi=STATEV(40)*PI/180.0D0phi2=STATEV(41)*PI/180.0D0!計算旋轉矩陣CALLEULER2ROT(phi1,Phi,phi2,Rot)!滑移驅動的旋轉角速度（簡化版：基面滑移主導旋轉）omega(1)=0.0D0omega(2)=0.0D0omega(3)=SUM(d_gamma(1:6))*1e-3!繞Z軸旋轉，比例系數校準!更新旋轉矩陣（小變形近似）Rot_new(1,1)=Rot(1,1)*COS(omega(3)*DTIME)-Rot(1,2)*SIN(omega(3)*DTIME)Rot_new(1,2)=Rot(1,1)*SIN(omega(3)*DTIME)+Rot(1,2)*COS(omega(3)*DTIME)Rot_new(1,3)=Rot(1,3)Rot_new(2,1)=Rot(2,1)*COS(omega(3)*DTIME)-Rot(2,2)*SIN(omega(3)*DTIME)Rot_new(2,2)=Rot(2,1)*SIN(omega(3)*DTIME)+Rot(2,2)*COS(omega(3)*DTIME)Rot_new(2,3)=Rot(2,3)Rot_new(3,:)=Rot(3,:)!旋轉矩陣轉回歐拉角CALLROT2EULER(Rot_new,phi1,Phi,phi2)!更新歐拉角狀態變量STATEV(39)=phi1*180.0D0/PISTATEV(40)=Phi*180.0D0/PISTATEV(41)=phi2*180.0D0/PI2.輔助子程序：旋轉矩陣轉歐拉角fortran!子程序：旋轉矩陣轉Z-X-Z歐拉角（適配HCP晶體）SUBROUTINEROT2EULER(Rot,phi1,Phi,phi2)REAL*8,INTENT(IN)::Rot(3,3)REAL*8,INTENT(OUT)::phi1,Phi,phi2REAL*8::eps=1e-6!計算Φ（極角）Phi=ACOS(Rot(3,3))IF(ABS(Phi)<eps.OR.ABS(Phi-PI)<eps)THEN!極角為0或π，歐拉角退化phi1=0.0D0phi2=ATAN2(-Rot(1,2),Rot(1,1))ELSE!通用情況phi1=ATAN2(Rot(1,3),-Rot(2,3))phi2=ATAN2(Rot(3,1),Rot(3,2))ENDIFENDSUBROUTINEROT2EULER三、Abaqus/CAE疲勞加載操作步驟步驟1：定義疲勞分析步進入Step模塊，創建Static,General分析步，勾選“Coupledtemperature-displacement”；設置分析步參數：時間總長：1000s（對應1000次循環，1s/循環）；自動步長：最小步長1e-6，最大步長1e-3；循環加載：通過*Amplitude定義正弦波應力幅值（如±200MPa）。步驟2：施加循環載荷與溫度邊界溫度載荷：恒定600℃（873K），通過*Temperature施加；循環應力載荷：進入Load模塊，選擇*Cload，施加Z向應力；關聯*Amplitude,NAME=Fatigue_Amp，定義正弦波：plaintext*Amplitude,Name=Fatigue_Amp0.0,0.01.0,200.02.0,-200.03.0,200.0...!循環至1000s約束條件：固定RVE模型的X/Y平動，釋放Z向位移（避免剛體轉動）。步驟3：輸出織構/疲勞結果變量進入Step模塊，編輯分析步的*Output,Field：勾選狀態變量（SDV）：SDV1-41（滑移應變、損傷、歐拉角）；勾選應力（S）、應變（E）、溫度（T）；設置輸出頻率：每10個增量步輸出一次（捕捉循環特征）。步驟4：提交作業與編譯bash運行abaqusjob=ti_hcp_fatigueinput=poly_ti.inpuser=umat_hcp_fatigue.f90-fortlib=/opt/intel/mkl/lib/intel64-cpus=8四、織構演化后處理（與EBSD對比）步驟1：提取歐拉角數據進入Visualization模塊，選擇Tools→XYData→Create→Element/Nodal；選擇“Statevariables”，提取SDV39-41（φ1,Φ,φ2），導出為txt文件。步驟2：ODF分析（與EBSD對比）將Abaqus導出的歐拉角數據導入MTEX（Matlab織構分析工具）；繪制ODF圖和極圖，對比EBSD實驗數據：matlab%MTEX代碼示例cs=crystalSymmetry('6/mmm',[2.954.68],'mineral','Ti');%HCP晶系euler=load('abaqus_euler.txt');%導入Abaqus歐拉角數據odf=calcODF(Euler(deg2rad(euler)),cs);%計算ODFplotODF(odf,'sections',6);%繪制ODF圖步驟3：疲勞損傷結果提取查看SDV38（損傷值）云圖，定位最先失效的晶粒；提取損傷值隨循環次數的曲線，擬合Manson-Coffin公式：Nf??γplc?=C（Nf?：疲勞壽命，γpl?：塑性剪切應變幅值，c：材料常數）。五、完整UMAT文件（疲勞+織構演化）fortran!UMATforHCPTifatigue+textureevolution(600℃)INCLUDE'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)!變量聲明REAL*8,PARAMETER::PI=3.141592653589793D0INTEGER,PARAMETER::NSYSTEM=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::C_elastic_inv(6,6),T_current,tau_cs_base,tau_cs_prismREAL*8::Q_base,Q_prism,T_ref,R,h_base,h_prismREAL*8::gamma_rev(NSYSTEM),cycle_num,gamma_amplitude,D,D_alpha(NSYSTEM)REAL*8::Rot(3,3),Rot_new(3,3),phi1,Phi,phi2,omega(3)INTEGER::i,j,alpha!步驟1：讀取參數T_ref=298.0D0R=8.314D0T_current=TEMP!步驟2：初始化狀態變量IF(KINC.EQ.1.AND.JSTEP.EQ.1)THEN!滑移應變、臨界分切應力DOalpha=1,NSYSTEMSTATEV(alpha)=0.0D0STATEV(alpha+NSYSTEM)=MERGE(PROPS(9),PROPS(10),alpha.LE.6)STATEV(alpha+24)=0.0D0!反向滑移應變ENDDOSTATEV(37)=0.0D0!循環次數STATEV(38)=0.0D0!損傷值STATEV(39:41)=[PROPS(22),PROPS(23),PROPS(24)]!初始歐拉角STATEV(40)=0.0D0!應力方向標記ENDIF!讀取狀態變量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+24)ENDDO!步驟3：構建HCP彈性剛度矩陣（損傷退化）CALLBUILD_C_ELASTIC_HCP(PROPS,C_elastic)IF(D>=PROPS(20))C_elastic=C_elastic*(1.0D0-D)!剛度退化!步驟4：初始化施密特矩陣（取向旋轉）CALLINIT_SCHMID_HCP(schmid,NSYSTEM)CALLEULER2ROT(phi1,Phi,phi2,Rot)!旋轉施密特矩陣schmid=MATMUL(schmid,Rot)!步驟5：計算分切應力DOalpha=1,NSYSTEMtau(alpha)=DOT_PRODUCT(schmid(alpha,:),STRESS(1:6))ENDDO!步驟6：計算剪切應變率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!步驟7：循環硬化+溫度依賴tau_cs_base=PROPS(14)*EXP(-PROPS(16)*1000.0D0/(R*T_current)+PROPS(16)*1000.0D0/(R*T_ref))tau_cs_prism=PROPS(15)*EXP(-PROPS(17)*1000.0D0/(R*T_current)+PROPS(17)*1000.0D0/(R*T_ref))DOalpha=1,NSYSTEMgamma_amplitude=ABS(gamma(alpha)-gamma_rev(alpha))IF(alpha.LE.6)THENh_base=PROPS(11)+PROPS(18)*cycle_num/PROPS(19)tau_c(alpha)=tau_cs_base-(tau_cs_base-PROPS(9))*EXP(-h_base*gamma(alpha))ELSEh_prism=PROPS(12)+PROPS(18)*cycle_num/PROPS(19)tau_c(alpha)=tau_cs_prism-(tau_cs_prism-PROPS(10))*EXP(-h_prism*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!步驟8：損傷演化DOalpha=1,NSYSTEMD_alpha(alpha)=PROPS(21)*(gamma_amplitude**2)*cycle_numENDDOD=D+MAXVAL(D_alpha)D=MIN(D,1.0D0)!損傷值不超過1!步驟9：塑性本構矩陣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)ENDDOENDDOENDIFENDDO!步驟10：彈塑性剛度矩陣CALLINV_MATRIX_6X6(C_elastic,C_elastic_inv)D_ep=C_elastic_inv+L_pCALLINV_MATRIX_6X6(D_ep,DDSDDE)!步驟11：更新應力DOi=1,6STRESS(i)=STRESS(i)+MATMUL(DDSDDE(i,:),DSTRAN(1:6))ENDDO!步驟12：取向旋轉更新CALLEULER2ROT(phi1,Phi,phi2,Rot)omega(3)=SUM(d_gamma(1:6))*1e-3Rot_new(1,1)=Rot(1,1)*COS(omega(3)*DTIME)-Rot(1,2)*SIN(omega(3)*DTIME)Rot_new(1,2)=Rot(1,1)*SIN(omega(3)*DTIME)+Rot(1,2)*COS(omega(3)*DTIME)Rot_new(1,3)=Rot(1,3)Rot_new(2,1)=Rot(2,1)*COS(omega(3)