PSI - Issue 14

C. Praveen et al. / Procedia Structural Integrity 14 (2019) 798–805 C. Praveen et al. / Structural Integrity Procedia 00 (2018) 000–000 C. Praveen t al. / Structural Integrity Procedia 00 (20 8) 000–000 . raveen et al. / Structural Integrity Procedia 00 (2018) 000–000

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In the second term of right hand side of Eq. (22) '  ' denotes the fourth order tensor. The implicit algorithm was written in Fortran language and the developed algorithm for calculating the stress increment for a given total strain increment is presented as flow chart in Fig. 1. Table 1. Values of the material constants in the equations used for calculation In the second term of right hand side of Eq. (22) '  ' denotes the fourth order tensor. The implicit algorithm was written in Fortran language and the developed algorithm for calculating the stress increment for a given total strain increment is presented as flow chart in Fig. 1. Table 1. Values of the material constants in the equations used for calculation I t sec ter f ri t a si e f . ( ) '  ' e tes t e f rt r er te s r. e i licit al rit s w itten in Fortran language t e e el e al rit f r calc lati t e stress i cre e t f r a i e t tal strai i cre e t is rese te as fl c art i i . . Table 1. Values of the material constants in the equations used for calculation

v v

k 2 k 2 k 2

I L I L I μm μm μm

s L s L s μm μm μm

L k L k L k

, f 0  , f 0  , f 0

0  0  0 

b b

 

Constants Constants sta ts

E E

M M

Units Units its Values Values Values

MPa MPa

- - -

- - - 3 3 3

- - -

m m

m –2 m –2 –2

MPa MPa MPa 272 272 272

- - -

- - -

210000 210000 210000

0.3 0.3 0.3

0.4 0.4 0.4

0.258 ×10 -9 0.258 ×10 -9 0.258 ×10 -9

1×10 11 1×10 11 1×10 11

0.18 20.4 5.8 27.6 0.18 20.4 5.8 27.6 0.18 20.4 5.8 27.6

Fig. 1. Algorithm to calculate stress increment for given strain increment using Euler backward implicit integration method. 3. Finite element analysis Commercial ABAQUS finite element analysis software was used to simulate the tensile deformation behaviour of U-notched geometry of circular cross-section with notch radii of 1.25, 2.5 and 5 mm. Eight-node quadratic axisymmetric element with reduced integration was used to model the specimen geometry. By considering the 2-dimensional axial symmetry along with symmetry plane in the middle of the specimen and the uniaxial loading condition, rectangle geometry with width equal to the specimen radius and height equal to half of the specimen length with only one notch has been chosen for the simulation as shown in Fig. 2. This geometry would help to reduce the number of total elements required for the simulation which results in reduction of solution convergence time. In order to ensure the size of mesh does not affect the finite element results, mesh convergence check has been carried out. Accordingly, finer mesh size has been chosen near to the notch root. The velocity boundary condition is given at the top of the specimen as 0.09 mm/s and other appropriate boundary conditions were applied to symmetry faces. The elasto-plastic material model in terms of user material subroutine has been provided to run the simulations for the given strain increment. The simulations were stopped after achieving the maximum nominal load in nominal stress-nominal strain curves. Fig. 1. Algorithm to calculate stress increment for given strain increment using Euler backward implicit integration method. 3. Finite element analysis Commercial ABAQUS finite element analysis software was used to simulate the tensile deformation behaviour of U-notched geometry of circular cross-section with notch radii of 1.25, 2.5 and 5 mm. Eight-node quadratic axisymmetric element with reduced integration was used to model the specimen geometry. By considering the 2-dimensional axial symmetry along with symmetry plane in the middle of the specimen and the uniaxial loading condition, rectangle geometry with width equal to the specimen radius and height equal to half of the specimen length with only one notch has been chosen for the simulation as shown in Fig. 2. This geometry would help to reduce the number of total elements required for the simulation which results in reduction of solution convergence time. In order to ensure the size of mesh does not affect the finite element results, mesh convergence check has been carried out. Accordingly, finer mesh size has been chosen near to the notch root. The velocity boundary condition is given at the top of the specimen as 0.09 mm/s and other appropriate boundary conditions were applied to symmetry faces. The elasto-plastic material model in terms of user material subroutine has been provided to run the simulations for the given strain increment. The simulations were stopped after achieving the maximum nominal load in nominal stress-nominal strain curves. i . . l rit t calc late stress i cre e t f r i e strain increment si ler ac ar i licit integration method. 3. i ite ele e t l sis C mmercial ABAQUS finite element analysis soft are was used t simulate the tensile deformation behavi r f - tc e e etr f circ lar cr ss-secti it tc ra ii f . , . a . i t- e quadratic axisymmetric element with reduced i tegration was used to model the specimen geometry. By considering the 2-dimensional axial sym etr al it s etr la e i t e i le f t e s eci e a t e ia ial l a i c iti , recta le etr it i th equal to the specimen radiu and ei t e al t alf of the specimen length with only one notch has been chosen for th simulation as shown in Fig. 2. This geometry would help to reduce the number of t tal elements required for the simulation which results in r d ction of solution convergence tim . In ord r to ensure the size of mesh does not affect t e fi ite element results, es c r e ce c ec as ee carrie t. cc r i l , fi er es size as ee c se ear t t e notc r t. e el cit ar c iti is i e at t e t f t e s eci e as . /s a t er appropriate bo ndary c iti s ere a lie t s etr faces. e elast - lastic aterial el i ter s f user material subroutin has be n provided to run the simulations for th given str in increment. The simulations ere st e after ac ie i t e a i i al l a in nominal stress- i al strai c r es.

Fig. 2. Representative figure of one-quarter of axisymmetric geometry with finite element mesh Fig. 2. Representative figure of one-quarter of axisymmetric geometry with finite element mesh i . . e rese tati e fi re f e- arter f a is etric e etr it fi ite ele e t es