def example4():
# T is in hours, strain in percent, stress in MPa
A = 1.85e-10
n = 2.5
m = 0.3
smodel = creep.PowerLawCreep(A, n)
cmodel = creep.J2CreepModel(smodel)
E = 150000.0
nu = 0.3
sY = 200.0
H = E / 25.0
elastic = elasticity.IsotropicLinearElasticModel(E, "youngs", nu,
"poissons")
surface = surfaces.IsoJ2()
iso = hardening.LinearIsotropicHardeningRule(sY, H)
flow = ri_flow.RateIndependentAssociativeFlow(surface, iso)
pmodel = models.SmallStrainRateIndependentPlasticity(elastic, flow)
model = models.SmallStrainCreepPlasticity(elastic, pmodel, cmodel)
res = drivers.creep(model, 205.0, 3600.0, 100.0, verbose = False,
nsteps_up = 500)
plt.plot(res['strain'], res['stress'])
plt.show()
def creep_ex():
E = 92000.0
nu = 0.3
s0 = 120.0
A = 1.0e-10
n = 3.0
Kp = E / 500
H = E / 500
smodel = creep.PowerLawCreep(A, n)
cmodel = creep.J2CreepModel(smodel)
elastic = elasticity.IsotropicLinearElasticModel(E, "youngs", nu,
"poissons")
surface = surfaces.IsoKinJ2()
iso = hardening.LinearIsotropicHardeningRule(s0, Kp)
kin = hardening.LinearKinematicHardeningRule(H)
hrule = hardening.CombinedHardeningRule(iso, kin)
flow = ri_flow.RateIndependentAssociativeFlow(surface, hrule)
pmodel = models.SmallStrainRateIndependentPlasticity(elastic, flow)
bmodel = models.SmallStrainCreepPlasticity(elastic, pmodel, cmodel)
A_damg = 1.0e-2
a_damg = 1.0
model = damage.NEMLPowerLawDamagedModel_sd(elastic,
A_damg,
a_damg,
bmodel,
verbose=False)
#res = drivers.uniaxial_test(model, 1.0e-2, emax = 0.25)
#plt.plot(res['strain'], res['stress'])
#plt.show()
res = drivers.creep(model, 120.0, 1.0, 393.0, verbose=False)
plt.plot(res['rtime'], res['rstrain'])
plt.show()
plt.loglog(res['rtime'], res['rrate'])
plt.show()
model = damage.ClassicalCreepDamageModel_sd(emodel, S, xi, phi, cmodel)
model2 = damage.ModularCreepDamageModel_sd(
emodel, S, xi, phi, damage.VonMisesEffectiveStress(), cmodel)
# Computed life
srange = np.linspace(s0 / 2, s0, 10)
tfs = S**(xi) / (1 + phi) * srange**(-xi)
slife = []
slife2 = []
for s, tf in zip(srange, tfs):
res = drivers.creep(model,
s,
srate,
tf * 1.25,
verbose=False,
logspace=False,
check_dmg=True,
nsteps=1000)
slife.append(res['rtime'][-1])
res2 = drivers.creep(model2,
s,
srate,
tf * 1.25,
verbose=False,
logspace=False,
check_dmg=True,
nsteps=1000)
slife2.append(res2['rtime'][-1])
plt.plot(srange, tfs / 3600.0, label="Analytic formula")
erate = 1.0e-4
hold = 1000.0 * 3600.0
res = drivers.stress_relaxation(model, emax, erate, hold)
plt.figure()
plt.plot(res['rtime'] / 3600.0, res['rstress'], 'k-')
plt.xlabel("Time (hrs)")
plt.ylabel("Stress (MPa)")
plt.title("Stress relaxation")
plt.tight_layout()
plt.show()
# Creep
smax = 180.0
srate = 1.0
hold = 10000.0 * 3600.0
res = drivers.creep(model, smax, srate, hold, logspace=True)
plt.figure()
plt.plot(res['rtime'] / 3600.0, res['rstrain'], 'k-')
plt.xlabel("Time (hrs)")
plt.ylabel("Creep strain (mm/mm)")
plt.title("Creep")
plt.tight_layout()
plt.show()
# Rate jump
erates = [1.0e-6, 1.0e-4, 1.0e-2, 1.0, 1.0e-2, 1.0e-4, 1.0e-6]
res = drivers.rate_jump_test(model, erates)
plt.figure()
plt.plot(res['strain'], res['stress'], 'k-')
plt.xlabel("Strain (mm/mm)")
plt.ylabel("Stress (MPa)")
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("Strain (-/-)")
plt.show()
# Stress relaxation test
res = drivers.stress_relaxation(model, 0.02, 1.0e-4, 2000.0)
plt.plot(res['time'], res['stress'], 'k-')
plt.xlabel('Time (s)')
plt.ylabel('Stress (MPa)')
plt.show()
plt.plot(res['rtime'], res['rrate'], 'k-')
plt.xlabel('Time (s)')
plt.ylabel('Relaxation rate (MPa/s)')
plt.show()
# Creep test
res = drivers.creep(model, 350.0, 10.0, 2000.0)
plt.plot(res['time'], res['strain'], 'k-')
plt.xlabel('Time (s)')
plt.ylabel('Strain (-/-)')
plt.show()
plt.plot(res['rtime'], res['rrate'], 'k-')
plt.xlabel('Time (s)')
plt.ylabel('Creep rate (1/s)')
plt.show()
smodel = creep.PowerLawCreep(A, n)
cmodel = creep.J2CreepModel(smodel)
E = 150000.0
nu = 0.3
sY = 200.0
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,
C = 28.0
lmr = larsonmiller.LarsonMillerRelation(fn, C)
estress = damage.VonMisesEffectiveStress()
model = damage.LarsonMillerCreepDamageModel_sd(emodel, lmr, estress,
bmodel)
T = 550 + 273.15
lmps = []
for s in srange:
res = drivers.creep(model,
s,
100.0,
300000 * 3600.0,
T=T,
check_dmg=True,
dtol=0.95,
nsteps_up=20,
nsteps=1000,
logspace=True)
time = res['rtime'][-1] / 3600.0
lmp = T * (np.log10(time) + base_C)
lmps.append(lmp)
plt.figure()
plt.semilogy(lmp_range,
10.0**np.polyval(base_poly, lmp_range),
'k-',
label="Base LMR")
plt.semilogy(lmps, srange, 'r--', label="Model results")
tf = 10000
# Hayhurst solution
times = np.linspace(0, tf, 100)
dmg = (1 - (eta + 1) * w0 * (s / s0)**nu * times)**(1.0 / (eta + 1.0))
strain = -e0 * (s / s0)**(-nu) * dmg**(eta + 1) / (
(1 + eta - n) * w0) * (s / (s0 * dmg))**n + e0 * (s / s0)**(n - nu) / (
(1 + eta - n) * w0)
E = 10000000.0
nu = 0.3
srate = 100.0
emodel = elasticity.IsotropicLinearElasticModel(E, "youngs", nu,
"poissons")
bmodel = models.SmallStrainElasticity(emodel)
scmodel = creep.NormalizedPowerLawCreep(s0, n)
cfmodel = creep.J2CreepModel(scmodel)
cmodel = models.SmallStrainCreepPlasticity(emodel, bmodel, cfmodel)
model = damage.ModularCreepDamageModel_sd(emodel, A, xi, phi,
damage.VonMisesEffectiveStress(),
cmodel)
res = drivers.creep(model, s, srate, tf, nsteps=1000)
plt.plot(times, strain)
plt.plot(res['rtime'], res['rstrain'])
plt.show()
plt.plot(res['cycles'], res['min'], 'k-')
plt.plot(res['cycles'], res['mean'], 'k-')
plt.xlabel("Cycle")
plt.ylabel("Strain (-/-)")
plt.show()
# Stress relaxation test
res = drivers.stress_relaxation(model, 0.02, 1.0e-4, 2000.0, verbose = False)
plt.plot(res['time'], res['stress'], 'k-')
plt.xlabel('Time (s)')
plt.ylabel('Stress (MPa)')
plt.show()
plt.plot(res['rtime'], res['rrate'], 'k-')
plt.xlabel('Time (s)')
plt.ylabel('Relaxation rate (MPa/s)')
plt.show()
# Creep test
res = drivers.creep(model, 150.0, 10.0, 6000.0)
plt.plot(res['time'], res['strain'], 'k-')
plt.xlabel('Time (s)')
plt.ylabel('Strain (-/-)')
plt.show()
plt.plot(res['rtime'], res['rrate'], 'k-')
plt.xlabel('Time (s)')
plt.ylabel('Creep rate (1/s)')
plt.show()