/COM,ANSYS MEDIA REL. 2024R2 (05/10/2024) REF. VERIF. MANUAL: REL. 2024R2 /VERIFY,VM316 /TITLE,VM316,J-INTEGRAL FOR A MIDDLE-CRACK TENSION SPECIMEN UNDER ELASTIC-PLASTIC DEFORMATION /COM, /COM, REFERENCE: ANDERSON,T.L.,"THE EPRI J-ESTIMATION PROCEDURE", IN /COM, FRACTURE MECHANICS: FUNDAMENTALS AND APPLICATIONS, CRC PRESS, /COM, 3RD EDITION, 2005, PG:398-444 /COM, /OUT,VM316_SCRATCH /COM, PARAMETER FOR CREATING THE CDB FILES TO STORE GEOMETRY AND MESH DATA /COM, _GEOMGEN = 0 ! SET TO 1 TO WRITE CDB FILES IF ANY INPUT FILE MODIFICATIONS !*********************************************************************************** ! PLANE STRESS !*********************************************************************************** ! REFERENCE RESULT FOR PLANE STRESS CONDITION !******************************************************** ! (ANDERSON,FRACTURE MECHANICS,2005,TABLE A9.11,PG-444) A=10 ! HALF CRACK LENGTH, MM W=4*A ! HALF WIDTH, MM E=200000 ! ELASTIC MODULUS, N/MM2 NU=0.3 ! POISSON'S RATIO PI=3.14159 ! RAMBERG-OSGOOD PARAMETERS SY=400 ! YIELD STRESS, MPA ALPHA=1.0 N=10 EY=SY/E P=22500 ! LOAD ON FULL GEOMETRY SPECIMEN, N/MM P0=2*(W-A)*SY ! LIMIT LOAD !---------------------------------------------- ! ELASTIC PART, JEL !---------------------------------------------- ! INITIAL ESTIMATE OF K1 FI=SQRT(1/COS(PI*A/(2*W))) K1I=(P/(2*W))*SQRT(PI*A)*FI ! EFFECTIVE CRACK LENGTH AFTER PLASTIC ZONE CORRECTION ! (ANDERSON,FRACTURE MECHANICS,2005,PG-400) BETA=2 ! 2 FOR PLANE STRESS, 6 FOR PLANE STRAIN AEFF=A+((N-1)/(N+1))*((K1I/SY)**2)/((BETA*PI)*(1+(P/P0)**2)) ! FINAL ESTIMATE OF K1 F=SQRT(1/COS(PI*AEFF/(2*W))) K1=(P/(2*W))*SQRT(PI*AEFF)*F ! JEL CALCULATION JEL=K1**2/E !---------------------------------------------- ! PLASTIC PART, JPL !---------------------------------------------- H1=2.86 ! FROM TABLE A9.11 (ANDERSON,FRACTURE MECHANICS) JPL=ALPHA*EY*SY*(W-A)*(A/W)*H1*(P/P0)**(N+1) !---------------------------------------------- ! TOTAL J = JEL + JPL !---------------------------------------------- J_REF_PS=JEL+JPL ! J, PLANE STRESS ! FRACTION OF JPL IN TOTAL J JPL_FRAC = JPL/J_REF_PS /OUT,VM316_SCRATCH,,,APPEND PARSAV !******************************************************** /PREP7 *IF,_GEOMGEN,EQ,1,THEN A=10 ! HALF CRACK LENGTH, MM W=4*A ! HALF WIDTH, MM L=5*W ! HALF LENGTH, MM E=200000 ! ELASTIC MODULUS, N/MM2 NU=0.3 ! POISSON'S RATIO PLOAD=P/2 ! HALF TENSILE LOAD, N/MM PRS=PLOAD/W ! TRACTION LOAD ON TOP FACE, N/MM ET,1,183 KEYOPT,1,3,0 ! PLANE STRESS=0, PLANE STRAIN=2 MP,EX,1,E MP,NUXY,1,NU ! RAMBERG-OSGOOD PARAMETERS SY=400 ! YIELD STRESS, MPA ALPHA=1.0 N=10 ! MISO PLASTICITY DEFINITION CLOSE TO RAMBERG-OSGOOD RELATION TB,PLAS,1,,,MISO TBPT,DEFI,0.0,300 ! PLASTIC STRAIN, STRESS TBPT,DEFI,5.26E-04,350 TBPT,DEFI,2.00E-03,400 TBPT,DEFI,3.67E-03,425 TBPT,DEFI,6.49E-03,450 TBPT,DEFI,1.12E-02,475 TBPT,DEFI,1.86E-02,500 TBPT,DEFI,3.03E-02,525 TBPT,DEFI,4.83E-02,550 TBPT,DEFI,7.54E-02,575 TBPT,DEFI,1.15E-01,600 TBPT,DEFI,1.73E-01,625 TBPT,DEFI,2.57E-01,650 TBPT,DEFI,3.75E-01,675 TBPT,DEFI,5.39E-01,700 TBPT,DEFI,7.65E-01,725 TBPT,DEFI,1.07,750 TBPT,DEFI,1.49,775 TBPT,DEFI,2.05,800 K,1, K,2,W-A K,3,W-A,L K,4,-A,L K,5,-A K,6,A K,7,A,A K,8,-A,A K,9,2*A K,10,2*A,2*A K,11,-A,2*A A,1,6,7,8,5 A,6,9,10,11,8,7 A,9,2,3,4,11,10 KSCON,1,A/16,0,8 ESIZE,A/16 AMESH,1 ESIZE,A/8 AMESH,2 ESIZE,A/4 AMESH,3 ALLSEL,ALL ! SYMMETRY CONDITIONS FOR LEFT AND BOTTOM FACES NSEL,S,LOC,X,-A DSYM,SYMM,X,0 ALLSEL,ALL NSEL,S,LOC,Y,0 NSEL,R,LOC,X,0,W-A DSYM,SYMM,Y,0 ALLSEL,ALL NSEL,S,LOC,Y,0 NSEL,R,LOC,X,0 ! CRACK-FRONT-NODE SELECTED CM,CRACK1,NODE ALLSEL,ALL ! DEFINE CRACK-EXTENSION DIRECTION CALCULATION-ASSIST NODE CASSIST=NODE(-A,0,0) CDWRITE,DB,vm316-1,cdb *ELSE CDREAD,DB,vm316-1,cdb *ENDIF FINISH !----------------------------------------------------------------------------------- /SOLU ANTYPE,STATIC OUTRES,NSOL,ALL OUTRES,CINT,ALL NSUBS,40,1000,40 TIME,1.0 ! LOADING ON TOP FACE NSEL,S,LOC,Y,L SF,ALL,PRES,-PRS ALLSEL,ALL ! JINT PARAMETER CINT,NEW,1 CINT,TYPE,JINT CINT,CTNC,CRACK1,CASSIST CINT,NCON,10 CINT,NORM,0,2 CINT,SYMM,ON ALLSEL,ALL SOLVE FINISH !----------------------------------------------------------------------------------- /POST1 ! J-INTEGRAL (AVERAGE, CONTOUR-2 TO 10) JAVG=0 *DO,NN,2,10 *GET,PVAL,CINT,1,CTIP,1,CONTOUR,NN,DTYPE,JINT JAVG = JAVG + PVAL/9 *ENDDO *DIM,LABEL,CHAR,1,2 *DIM,VALUE,,1,3 LABEL(1,1)='JINT' *VFILL,VALUE(1,1),DATA,J_REF_PS *VFILL,VALUE(1,2),DATA,JAVG *VFILL,VALUE(1,3),DATA,J_REF_PS/JAVG SAVE,TABLE_1 FINISH /CLEAR,NOSTART !*********************************************************************************** ! PLANE STRAIN !*********************************************************************************** /OUT,VM316_SCRATCH,,,APPEND PARRES,CHANGE ! REFERENCE RESULT FOR PLANE STRAIN CONDITION !******************************************************** ! (ANDERSON,FRACTURE MECHANICS,2005,TABLE A9.10,PG-443) A=10 ! HALF CRACK LENGTH, MM W=4*A ! HALF WIDTH, MM E=200000 ! ELASTIC MODULUS, N/MM2 NU=0.3 ! POISSON'S RATIO PI=3.14159 ! RAMBERG-OSGOOD PARAMETERS SY=400 ! YIELD STRESS, MPA ALPHA=1.0 N=10 EY=SY/E P=22500 ! LOAD ON FULL GEOMETRY SPECIMEN, N/MM P0=(4/SQRT(3))*(W-A)*SY ! LIMIT LOAD !---------------------------------------------- ! ELASTIC PART, JEL !---------------------------------------------- ! INITIAL ESTIMATE OF K1 FI=SQRT(1/COS(PI*A/(2*W))) K1I=(P/(2*W))*SQRT(PI*A)*FI ! EFFECTIVE CRACK LENGTH AFTER PLASTIC ZONE CORRECTION ! (ANDERSON,FRACTURE MECHANICS,2005,PG-400) BETA=6 ! 2 FOR PLANE STRESS, 6 FOR PLANE STRAIN AEFF=A+((N-1)/(N+1))*((K1I/SY)**2)/((BETA*PI)*(1+(P/P0)**2)) ! FINAL ESTIMATE OF K1 F=SQRT(1/COS(PI*AEFF/(2*W))) K1=(P/(2*W))*SQRT(PI*AEFF)*F ! JEL CALCULATION JEL=(1-NU**2)*K1**2/E !---------------------------------------------- ! PLASTIC PART, JPL !---------------------------------------------- H1=2.92 ! FROM TABLE A9.10 (ANDERSON,FRACTURE MECHANICS) JPL=ALPHA*EY*SY*(W-A)*(A/W)*H1*(P/P0)**(N+1) !---------------------------------------------- ! TOTAL J = JEL + JPL !---------------------------------------------- J_REF_PE=JEL+JPL ! J, PLANE STRAIN ! FRACTION OF JPL IN TOTAL J JPL_FRAC = JPL/J_REF_PE /OUT,VM316_SCRATCH,,,APPEND PARSAV !******************************************************** /PREP7 *IF,_GEOMGEN,EQ,1,THEN A=10 ! HALF CRACK LENGTH, MM W=4*A ! HALF WIDTH, MM L=5*W ! HALF LENGTH, MM E=200000 ! ELASTIC MODULUS, N/MM2 NU=0.3 ! POISSON'S RATIO PLOAD=P/2 ! HALF TENSILE LOAD, N/MM PRS=PLOAD/W ! TRACTION LOAD ON TOP FACE, N/MM ET,1,183 KEYOPT,1,3,2 ! PLANE STRESS=0, PLANE STRAIN=2 MP,EX,1,E MP,NUXY,1,NU ! RAMBERG-OSGOOD PARAMETERS SY=400 ! YIELD STRESS, MPA ALPHA=1.0 N=10 ! MISO PLASTICITY DEFINITION CLOSE TO RAMBERG-OSGOOD RELATION TB,PLAS,1,,,MISO TBPT,DEFI,0.0,300 ! PLASTIC STRAIN, STRESS TBPT,DEFI,5.26E-04,350 TBPT,DEFI,2.00E-03,400 TBPT,DEFI,3.67E-03,425 TBPT,DEFI,6.49E-03,450 TBPT,DEFI,1.12E-02,475 TBPT,DEFI,1.86E-02,500 TBPT,DEFI,3.03E-02,525 TBPT,DEFI,4.83E-02,550 TBPT,DEFI,7.54E-02,575 TBPT,DEFI,1.15E-01,600 TBPT,DEFI,1.73E-01,625 TBPT,DEFI,2.57E-01,650 TBPT,DEFI,3.75E-01,675 TBPT,DEFI,5.39E-01,700 TBPT,DEFI,7.65E-01,725 TBPT,DEFI,1.07,750 TBPT,DEFI,1.49,775 TBPT,DEFI,2.05,800 K,1, K,2,W-A K,3,W-A,L K,4,-A,L K,5,-A K,6,A K,7,A,A K,8,-A,A K,9,2*A K,10,2*A,2*A K,11,-A,2*A A,1,6,7,8,5 A,6,9,10,11,8,7 A,9,2,3,4,11,10 KSCON,1,A/16,0,8 ESIZE,A/16 AMESH,1 ESIZE,A/8 AMESH,2 ESIZE,A/4 AMESH,3 ALLSEL,ALL ! SYMMETRY CONDITIONS FOR LEFT AND BOTTOM FACES NSEL,S,LOC,X,-A DSYM,SYMM,X,0 ALLSEL,ALL NSEL,S,LOC,Y,0 NSEL,R,LOC,X,0,W-A DSYM,SYMM,Y,0 ALLSEL,ALL NSEL,S,LOC,Y,0 NSEL,R,LOC,X,0 ! CRACK-FRONT-NODE SELECTED CM,CRACK1,NODE ALLSEL,ALL ! DEFINE CRACK-EXTENSION DIRECTION CALCULATION-ASSIST NODE CASSIST=NODE(-A,0,0) CDWRITE,DB,vm316-2,cdb *ELSE CDREAD,DB,vm316-2,cdb *ENDIF FINISH !----------------------------------------------------------------------------------- /SOLU ANTYPE,STATIC OUTRES,NSOL,ALL OUTRES,CINT,ALL NSUBS,40,1000,40 TIME,1.0 ! LOADING ON TOP FACE NSEL,S,LOC,Y,L SF,ALL,PRES,-PRS ALLSEL,ALL ! JINT PARAMETER CINT,NEW,1 CINT,TYPE,JINT CINT,CTNC,CRACK1,CASSIST CINT,NCON,10 CINT,NORM,0,2 CINT,SYMM,ON ALLSEL,ALL SOLVE FINISH !----------------------------------------------------------------------------------- /POST1 ! J-INTEGRAL (AVERAGE, CONTOUR-2 TO 10) JAVG=0 *DO,NN,2,10 *GET,PVAL,CINT,1,CTIP,1,CONTOUR,NN,DTYPE,JINT JAVG = JAVG + PVAL/9 *ENDDO *DIM,LABEL,CHAR,1,2 *DIM,VALUE,,1,3 LABEL(1,1)='JINT' *VFILL,VALUE(1,1),DATA,J_REF_PE *VFILL,VALUE(1,2),DATA,JAVG *VFILL,VALUE(1,3),DATA,J_REF_PE/JAVG SAVE,TABLE_2 FINISH !*********************************************************************************** RESUME,TABLE_1 /OUT,vm316,vrt /COM, /COM, ----------------------- VM316 RESULT COMPARISON -------------------------- /COM, /COM, | TARGET | MECHANICAL APDL | RATIO /COM, /COM, PLANE STRESS /COM, *VWRITE,LABEL(1,1),VALUE(1,1),VALUE(1,2),VALUE(1,3) (1X,A14,' ',E12.3,' ',E12.3,' ',F12.3) /COM, /COM, /NOPR, RESUME,TABLE_2 /COM, /COM, /COM, PLANE STRAIN /COM, *VWRITE,LABEL(1,1),VALUE(1,1),VALUE(1,2),VALUE(1,3) (1X,A14,' ',E12.3,' ',E12.3,' ',F12.3) /COM, /COM, /COM, -------------------------------------------------------------------------- /OUT, *LIST,vm316,vrt /OUT,VM316_SCRATCH,,,APPEND /DELETE,TABLE_1 /DELETE,TABLE_2