Most of the mechanical components are generally designed to respond in their elastic manner (A-B) during their lifetime. In such cases only the modulus of Elasticity E, poison ratio ν, and the value of Yield stress σy including some safety factor are sufficient input material data in order to perform Finite Element Analysis (assuming isotropic homogenous material). If the stresses in the simulation appear to be higher than the yield stress, material starts yielding. If we like to stay in the elastic region we have two options in offer; to change the geometry or take stronger material. (If dynamic analysis is performed Dynamic Yield stress should be used)
However…..real challenge comes after the yielding B point !!!
Designing in the elastic response can lead into massive structures in cases where possibility of high intensity loads can appear once in a lifetime of a product. Just imagine how massive car should be to avoid plastic deformation during an accident. In material processing analyses like sheet metal forming, we also need to analyze material behavior beyond the yield stress. So additionally we need to describe the plastic part of the stress-strain curve (B-D). The simplest approximation is bi-linear curve which after the yield stress is defined with the tangent modulus Et. For more precise analysis more complicated models can be used. After the yield point (B-C), cross-section area cannot be approximated with its initial value A0, therefore engineering stress strain curve should be corrected using true (logarithm) stress strain curve for higher precision. When the maximum force is reached (at the onset of necking (point C)) the specimen deformation is considerably localized, uni-axial stress state is replaced with multiaxial one. So here (C-D), correction of the stress should be done using Bridgman’s equation and strain has to be calculated based on the change of sample diameter and not change of length. Additionally the modulus of elasticity E, also changes with deformation. (If dynamic FE analysis is performed, dynamic tests should be done additionally in order to determine coefficients describing the influence of strain rate on flow stress. Cowper-Symonds and Johnson-Cook material models are most often used)
In some other cases, we are interested in precise prediction of fracture appearance its development and final size. Examples can be fatigue fracture analysis of cyclic loading of gears or dynamic plate perforation, blast response simulations etc. Here beside the constitutive model (stress-strain curve) we have to define fracture model and to provide appropriate material coefficients. This again requires additional tests to be performed depending on the suitable fracture model.
In the next few videos, simulation of fracture prediction in tensile test is presented. Material parameters for Johnson-Cook strength and fracture models for armour steel PROTAC 500 were previously determined based on combination of experimental test and numerical analyses. Simulation results were compared with the experimental one for tensile specimens with different initial Stress Triaxiality Ratios, showing very good agreement.
Movies of the tensile tests simulations with different initial stress triaxiality ratios
$# LS-DYNA Keyword file created by LS-PrePost 4.0 - 14Apr2013(16:00)
$# Created on Nov-27-2013 (10:15:55)
*KEYWORD
*TITLE
$# title
*CONTROL_ENERGY
$# hgen rwen slnten rylen
2 1 1 1
*CONTROL_TERMINATION
$# endtim endcyc dtmin endeng endmas
261.00000 0 0.000 0.000 0.000
*CONTROL_TIMESTEP
$# dtinit tssfac isdo tslimt dt2ms lctm erode ms1st
0.000 1.000000 0 0.000 0.010000 0 0 0
$# dt2msf dt2mslc imscl unused unused rmscl
0.000 0 0 0.000
*DATABASE_ELOUT
$# dt binary lcur ioopt option1 option2 option3 option4
1.000000 0 0 1 0 0 0 0
*DATABASE_GLSTAT
$# dt binary lcur ioopt
1.000000 0 0 1
*DATABASE_MATSUM
$# dt binary lcur ioopt
1.000000 0 0 1
*DATABASE_NODOUT
$# dt binary lcur ioopt option1 option2
1.000000 0 0 1 0.000 0
*DATABASE_SPCFORC
$# dt binary lcur ioopt
1.000000 0 0 1
*DATABASE_BINARY_D3PLOT
$# dt lcdt beam npltc psetid
1.000000 0 0 0 0
$# ioopt
0
*BOUNDARY_PRESCRIBED_MOTION_SET
$# nsid dof vad lcid sf vid death birth
2 1 2 1 1.000000 01.0000E+28 0.000
*BOUNDARY_SPC_SET
$# nsid cid dofx dofy dofz dofrx dofry dofrz
1 0 1 1 1 0 0 0
*PART
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ PARTS DEFINITIONS $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$# title
Solid
$# pid secid mid eosid hgid grav adpopt tmid
1 1 1 2 1 0 0 0
*SECTION_SOLID
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ SECTION DEFINITIONS $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$# secid elform aet
1 2 0
*MAT_JOHNSON_COOK
$# mid ro g e pr dtf vp rateop
1 7850.00007.3000E+101.9000E+11 0.300000 0.000 0.000 0.000
$# a b n c m tm tr epso
7.5000E+8 5.7100E+8 0.210000 0.003900 0.912000 1820.0000 293.00000 1.000000
$# cp pc spall it d1 d2 d3 d4
455.00000 0.000 2.000000 0.000 1.4000E-4 1.285000 -1.916000 0.000
$# d5 c2/p erod efmin
0.000 0.000 0 0.000
*EOS_LINEAR_POLYNOMIAL
$# eosid c0 c1 c2 c3 c4 c5 c6
2 0.0001.7200E+11 0.000 0.000 0.000 0.000 0.000
$# e0 v0
0.000 0.000
*HOURGLASS
$# hgid ihq qm ibq q1 q2 qb/vdc qw
1 3 0.100000 0 1.500000 0.060000 0.100000 0.100000
*DEFINE_CURVE
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$ LOAD DEFINITIONS $
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$# lcid sidr sfa sfo offa offo dattyp
1 0 0.000 0.000 0.000 0.000 0
$# a1 o1
0.000 0.000
50.000000 3.701000e-004
100.00000 0.001110
200.00000 0.002961
262.00000 0.003879
*DAMPING_GLOBAL
$# lcid valdmp stx sty stz srx sry srz
0 1.000000 0.000 0.000 0.000 0.000 0.000 0.000
*END
Change DT2MS in CONTROL_TIMESTEP to lower values when simulating quasi-static tension test with the explicit solver (Plot the Kinetic and Internal Energies. The kinetic energy should be a small fraction of the Internal energy for the deforming material when doing Quasi-static simulation with explicit code. (Be aware that lower values of DT2MS will increase the computational time). For more info about mass scaling visit http://blog2.d3view.com/overview-of-mass-scaling/
Hello,
ReplyDeleteI find this material useful. I am looking to simulate a pull out test for a glass coating on titanium. can you please assist on how to go about it?