def verify_warp3d():
E = 30000.0
nu = 0.3
sy = 100.0
Q = 50.0
b = 100.0
C = 1000.0
g = 10.0
mu = E / (2 * (1.0 + nu))
K = E / (3 * (1 - 2 * nu))
elastic = elasticity.IsotropicLinearElasticModel(mu, "shear", K, "bulk")
surface = surfaces.IsoKinJ2()
iso = hardening.VoceIsotropicHardeningRule(sy, Q, b)
hrule = hardening.Chaboche(iso, [C], [hardening.ConstantGamma(g)], [0.0],
[1.0])
flow = ri_flow.RateIndependentNonAssociativeHardening(surface, hrule)
model = models.SmallStrainRateIndependentPlasticity(elastic,
flow,
verbose=False)
res = drivers.strain_cyclic(model, 0.0075, -1.0, 1.0e-4, 50)
strain = res['strain']
stress = res['stress']
data_warp = np.load('data_fa_warp.npy')
plt.plot(strain, stress, 'k-')
plt.plot(data_warp[0], data_warp[1], 'r-')
plt.show()
def verify_Cg():
E = 30000.0
nu = 0.3
sy = 100.0
Q = 0.0
b = 0.0
C = 1000.0
g = 10.0
mu = E / (2 * (1.0 + nu))
K = E / (3 * (1 - 2 * nu))
elastic = elasticity.IsotropicLinearElasticModel(mu, "shear", K, "bulk")
surface = surfaces.IsoKinJ2()
iso = hardening.VoceIsotropicHardeningRule(sy, Q, b)
hrule = hardening.Chaboche(iso, [C], [hardening.ConstantGamma(g)], [0.0],
[1.0])
flow = ri_flow.RateIndependentNonAssociativeHardening(surface, hrule)
model = models.SmallStrainRateIndependentPlasticity(elastic,
flow,
verbose=False)
res = drivers.strain_cyclic(model, 0.4, -1.0, 1.0e-4, 1)
strain = res['strain']
stress = res['stress']
mv = np.max(np.abs(stress))
hu = mv - sy
print("C/y: %f / %f" % ((C / g), hu))
plt.figure()
plt.plot(res['strain'], res['stress'], 'k-')
plt.xlabel("Strain (mm/mm)")
plt.ylabel("Stress (MPa)")
plt.title("Uniaxial tension")
plt.show()
# Strain controlled-cyclic
emax = 0.01
R = -0.75
erate = 1.0e-4
ncycles = 5
hold_time = [10 * 3600.0, 0]
res = drivers.strain_cyclic(model,
emax,
R,
erate,
ncycles,
hold_time=hold_time)
plt.figure()
plt.plot(res['strain'], res['stress'], 'k-')
plt.xlabel("Strain (mm/mm)")
plt.ylabel("Stress (MPa)")
plt.title("Strain-controlled cyclic")
plt.show()
# Strain controlled-cyclic with follow up
emax = 0.01
R = -0.75
erate = 1.0e-4
ncycles = 5
hold_time = [10 * 3600.0, 0]
unit_extrapolate=10,
allowable_jump_stress=10.0,
jump_delta_N=10,
check_dmg=True)
end = time.time()
time_ext.append(end - start)
plt.plot(res['cycles'],
res['max'],
'+',
label='ext run {}'.format(r + 1))
plt.plot(res['cycles'], res['min'], '+')
start = time.time()
res = drivers.strain_cyclic(model,
emax[r],
R[r],
erate[r],
int(ncycles[r]),
hold_time=[hold_t[r], hold_c[r]],
check_dmg=True)
end = time.time()
time_act.append(end - start)
plt.plot(res['cycles'], res['max'], label='act run {}'.format(r + 1))
plt.plot(res['cycles'], res['min'])
plt.legend(loc='best')
plt.xlabel('cycles')
plt.ylabel('stress')
plt.title('Extrapolation comparison with damage')
plt.show()
plt.scatter(np.arange(len(emax)), time_act, label='act')
plt.scatter(np.arange(len(emax)), time_ext, marker='^', label='ext')
plt.yscale('log')
flow,
verbose=False,
check_kt=False)
# Uniaxial stress/strain curves at decades of strain rates
erates = np.logspace(-6, 2, 9)
for rate in erates:
res = drivers.uniaxial_test(model, rate)
plt.plot(res['strain'], res['stress'])
plt.xlabel("Strain (-/-)")
plt.ylabel("Stress (MPa)")
plt.show()
# A strain-controlled cyclic test
res = drivers.strain_cyclic(model, 0.01, -0.25, 1.0e-4, 50)
plt.plot(res['strain'], res['stress'], 'k-')
plt.xlabel("Strain (-/-)")
plt.ylabel("Stress (MPa)")
plt.show()
plt.plot(res['cycles'], res['max'], 'k-')
plt.plot(res['cycles'], res['min'], 'k-')
plt.plot(res['cycles'], res['mean'], 'k-')
plt.xlabel("Cycle")
plt.ylabel("Stress (MPa)")
plt.show()
# A stress-controlled cyclic test
res = drivers.stress_cyclic(model, 525.0, -1.0, 5.0, 50, hold_time=100)
plt.plot(res['strain'], res['stress'], 'k-')
elastic = elasticity.IsotropicLinearElasticModel(E, "youngs", nu,
"poissons")
surface = surfaces.IsoJ2()
pmodel = models.SmallStrainPerfectPlasticity(elastic, surface, sY)
model = models.SmallStrainCreepPlasticity(elastic, pmodel, cmodel)
res = drivers.creep(model, 200.0, 1.0e2, 1000.0, verbose=True)
plt.plot(res['time'], res['strain'])
plt.show()
res = drivers.strain_cyclic(model,
0.01,
-1,
1.0e-4,
15,
verbose=True,
nsteps=25,
hold_time=[10.0, 0])
plt.plot(res['strain'], res['stress'])
plt.show()
res = drivers.uniaxial_test(model,
1.0e-6,
sdir=np.array([1, -1, 0.5, -0.5, 0.1, -0.25]),
verbose=True)
plt.plot(res['strain'], res['stress'])
plt.show()
strength435 = sliprules.KinematicPowerLawSlipRule(h4, h3, h8, g0, n)
def make_model(smodel):
imodel = inelasticity.AsaroInelasticity(smodel)
emodel = elasticity.IsotropicLinearElasticModel(E, "youngs", nu, "poissons")
kmodel = kinematics.StandardKinematicModel(emodel, imodel)
model = singlecrystal.SingleCrystalModel(kmodel, lattice)
return polycrystal.TaylorModel(model, orientations, nthreads = nthreads)
# Perfect plasticity options
smodels = [strength775, strength766]
names = ["775", "766"]
models = [make_model(s) for s in smodels]
results = [drivers.strain_cyclic(m, emax, R, erate, ncycles, verbose = True)
for m in models]
plt.figure()
plt.title("Various perfect plasticity options")
for res, name in zip(results, names):
plt.plot(res['strain'], res['stress'], label = name)
plt.legend(loc='best')
plt.xlabel("Strain (mm/mm)")
plt.ylabel("Stress (MPa)")
plt.show()
# Pure isotropic options
smodels = [strength771, strength722, strength735]
names = ["771", "722", "735"]
def koo():
# Data from Koo & Kwon (2011)
E = 157.0e3
nu = 0.27
sY = 0.0
b = 3.0
Q = -80.0
C1 = 135.0e3
C2 = 123.0e3
C3 = 4.0e3
g1 = 100e3
g2 = 0.85e3
g3 = 1.0
eta = 701.0
n = 10.5
mu = E / (2 * (1.0 + nu))
K = E / (3 * (1 - 2 * nu))
elastic = elasticity.IsotropicLinearElasticModel(mu, "shear", K, "bulk")
surface = surfaces.IsoKinJ2()
iso = hardening.VoceIsotropicHardeningRule(sY, Q, b)
cs = [C1, C2, C3]
gs = [hardening.ConstantGamma(g1), hardening.ConstantGamma(g2),
hardening.ConstantGamma(g3)]
hmodel = hardening.Chaboche(iso, cs, gs, [0.0]*len(cs), [1.0]*len(cs))
fluidity = visco_flow.ConstantFluidity(eta)
vmodel = visco_flow.ChabocheFlowRule(
surface, hmodel, fluidity, n)
flow = general_flow.TVPFlowRule(elastic, vmodel)
model = models.GeneralIntegrator(elastic, flow)
e500 = np.array([0.0058793164, 0.0052876081, 0.004710156, 0.0042916722, 0.0038731605, 0.0032237573, 0.0027900399, 0.0024864991, 0.0017489338, 0.000635346, -0.0006668255, -0.0017811254, -0.0034891722, -0.0044012326, -0.0059358454, -0.005661599, -0.0051996206, -0.0048027165, -0.0044347716, -0.0039945684, -0.0034388636, -0.0032440594, -0.0026585856, -0.002036857, -0.001161945, -0.0003736313, 0.0008344368, 0.0022454705, 0.0035554683, 0.0052854997])
s500 = np.array([349.6965238343, 255.0932943767, 171.2928564634, 102.3697757811, 34.7967386021, -70.6166129529, -103.0909625627, -128.7931029969, -172.1191145041, -237.1093535238, -285.2558144812, -315.8199441656, -342.4341275638, -350.0133084444, -361.0726693423, -319.1748939033, -252.9445696747, -190.7753717856, -128.6110609317, -59.6843149729, 25.4625011672, 57.8965327357, 103.8969743143, 147.2034376803, 200.6779888803, 240.6374439409, 288.0930002819, 323.4323743399, 343.229143486, 357.0215788789])
res = drivers.strain_cyclic(model, 0.006, -1.0, 1.0e-4, 130,
verbose = False, nsteps = 50)
plt.plot(res['strain'][-100:], res['stress'][-100:], 'k-')
plt.plot(e500, s500, 'kx')
plt.xlabel("Strain (-/-)")
plt.ylabel("Stress (MPa)")
plt.show()
n500 = np.array([1.8000456006, 7.2646606231, 17.3775914892, 25.6289731945, 35.040864809, 43.9864865417, 54.6731673353, 69.3076477381, 83.9405590891, 98.1077889527, 112.0424068927, 126.7891398736])
ns500 = sn500 = np.array([437.8476941068, 428.2481618804, 413.6055992266, 403.8518586317, 394.8643791744, 388.2393032756, 382.3835530687, 376.4641827161, 372.5718311079, 370.2817510291, 368.4971998147, 367.5615301197])
plt.plot(res['cycles'], res['max'], 'k-')
plt.plot(n500, ns500, 'kx')
plt.xlabel("Cycle")
plt.ylabel("Stress (MPa)")
plt.show()
flow = general_flow.TVPFlowRule(elastic, vmodel)
model = models.GeneralIntegrator(elastic, flow, verbose = False)
# Uniaxial stress/strain curves at decades of strain rates
erates = np.logspace(-6,2,9)
for rate in erates:
res = drivers.uniaxial_test(model, rate, verbose = False)
plt.plot(res['strain'], res['stress'])
plt.xlabel("Strain (-/-)")
plt.ylabel("Stress (MPa)")
plt.show()
# A strain-controlled cyclic test
res = drivers.strain_cyclic(model, 0.001, -0.25, 1.0e-4, 50,
verbose = False)
plt.plot(res['strain'], res['stress'], 'k-')
plt.xlabel("Strain (-/-)")
plt.ylabel("Stress (MPa)")
plt.show()
plt.plot(res['cycles'], res['max'], 'k-')
plt.plot(res['cycles'], res['min'], 'k-')
plt.plot(res['cycles'], res['mean'], 'k-')
plt.xlabel("Cycle")
plt.ylabel("Stress (MPa)")
plt.show()
# A stress-controlled cyclic test
res = drivers.stress_cyclic(model, 100.0, -1.0, 5.0, 50,
hold_time = 10, verbose = False)
