def predict(self, c_p, m_p, method='tanaka'):
# usage：完成预测过程，输出SIF变幅、FCGR、循环次数、有效性判定
# NOTE：参数全部引用自函数外部，不适合从其它文件调用
# input parameter：
# load：实验施加的载荷峰值，应当为1个数，可从外部的数组中取一个调用
# return parameter：
# cracklength：给定的裂纹长度，mm
# dk_predict：计算的SIF变幅，Mpa.m0.5
# dadn：估计的FCGR，mm/cycles
# valid：有效性判断结果
_ = self.evaluate_sif_range_k1()
_ = self.evaluate_sif_range_k2()
_ = self.calculate_sif_range_eff(method=method)
self.fcg_rate = mts_analysis.ParisCalculating(c=c_p,
m=m_p,
dk=self.sif_range_eff)
self.cycle = experiment_predict.CycleIntegrateBySimpson(
c=c_p, m=m_p, dk=self.sif_range_eff, cracklength=self.cracklength)
for seq, value in enumerate(self.cracklength):
self.valid.append(
mts_analysis.LigamentValidCheck(w=self.width,
a=value,
dk=self.sif_range_eff[seq],
ys=self.yieldstrength,
r=self.stressratio))
return self.cracklength, self.sif_range_eff, self.fcg_rate, self.cycle, self.valid
def AlphaCalculate(fade_rate,
amplitude,
dadn,
dk,
kc,
a,
a_range,
a_amplitude,
stress_ratio,
numofaverage=7,
error_ratio=0.2):
# 放弃
# 移动平均
kc_Manual_averaged2, dk_Manual_averaged2 = \
DoubleDataSelectMovingAverage(data=kc, reference=dk,
ratio=error_ratio, numofaverage=numofaverage)
_, a_Manual_averaged2 = \
DoubleDataSelectMovingAverage(data=kc, reference=a,
ratio=error_ratio, numofaverage=numofaverage)
_, dadn_Manual_averaged2 = \
DoubleDataSelectMovingAverage(data=kc, reference=dadn,
ratio=error_ratio, numofaverage=numofaverage)
# 数据筛选a_range
dadn_selecting_average2, dk_selecting_averaged2, kc_selecting_averaged2, a_selecting_averaged2 = \
mts_analysis.FCGDataSelectByThreshold(dadn=dadn_Manual_averaged2, dk=dk_Manual_averaged2,
n=kc_Manual_averaged2, a=a_Manual_averaged2,
threshold=a_range[0], target='a', keepbigger=1)
dadn_selected_averaged2, dk_selected_averaged2, kc_selected_averaged2, a_selected_averaged2 = \
mts_analysis.FCGDataSelectByThreshold(dadn=dadn_selecting_average2, dk=dk_selecting_averaged2,
n=kc_selecting_averaged2, a=a_selecting_averaged2,
threshold=a_range[1], target='a', keepbigger=0)
# 拟合数据准备
kmin_selected_averaged2 = dk_selected_averaged2 * (
stress_ratio / (1 - stress_ratio)) # Kmin计算
kmax_selected_averaged2 = dk_selected_averaged2 * (1 / (1 - stress_ratio)
) # Kmax计算
c_p, m_p = paris_and_walker.ParisParameter(r=stress_ratio) # Paris参数读取
betas = (a_selected_averaged2 - a_amplitude) / a_amplitude # 裂纹长度无量纲量
# 计算参数alpha
alpha_e = []
for beta in betas:
if beta < 0:
alpha_e.append(2 / np.pi)
else:
alpha_e.append(amplitude * np.exp(-fade_rate * beta))
alpha_e = np.array(alpha_e)
# 基于参数计算有效应力强度因子
dkeff_alpha_e = kmax_selected_averaged2 - alpha_e * kc_selected_averaged2 - (
1 - alpha_e) * kmin_selected_averaged2
# 计算dadn
dadn_alpha_e = mts_analysis.ParisCalculating(c=c_p,
m=m_p,
dk=dkeff_alpha_e)
return dk_selected_averaged2, dkeff_alpha_e, dadn_alpha_e, alpha_e, betas, a_selected_averaged2
def evaluate_fcg_rate_by_paris(self, c_p, m_p):
self.fcg_rate = mts_analysis.ParisCalculating(c=c_p,
m=m_p,
dk=self.sif_range_eff)
return self.fcg_rate
'''
数据读取处理
'''
specimen_data = []
for sequence in sequences:
specimen_data.append(
mts_class.SpecimenBasic(name=sequence, stress_ratio=r,
threshold=0)) # 创建实例
for specimen in specimen_data:
specimen.read_experimental_data() # 读取和计算
'''
Paris拟合和Walker模型效果对比
'''
dadn_paris_Manual = mts_analysis.ParisCalculating(c=c_p,
m=m_p,
dk=np.array(
specimen.dk_Manual))
'''
数据保存
'''
if filesave:
for specimen in specimen_data:
data = np.array([
specimen.n_Manual, specimen.a_Manual, specimen.dk_Manual,
specimen.dadn_Manual, specimen.kc_Manual
])
name = [
"Original_Cycles", "Original_CrackLength/mm",
"Original_SIFRange/MPam0.5", "Original_FCGRate/mm per cycle",
"Original_ClosureSIF/MPam0.5"
]
# dkeff计算
dkeff_Manual_2pi = closureanalysis.dKeffCalculation(kmax=dk_Manual / (1 - r),
kclose=kc_Manual,
kmin=dk_Manual * (r /
(1 - r)),
method='2/PI')
# 移动平均
dkeff_Manual_averaged0, dk_Manual_averaged0 = \
closureanalysis.DoubleDataSelectMovingAverage(data=dkeff_Manual_2pi, reference=dk_Manual,
ratio=ratio, numofaverage=numofaverage)
_, a_Manual_averaged0 = \
closureanalysis.DoubleDataSelectMovingAverage(data=dkeff_Manual_2pi, reference=a_Manual,
ratio=ratio, numofaverage=numofaverage)
# 计算基于裂纹闭合效应的dadn(2/PI法)
dadn_paris_dkeff_2pi = mts_analysis.ParisCalculating(c=c_p,
m=m_p,
dk=dkeff_Manual_averaged0)
'''
传统dkeff法(basic)
'''
# dkeff计算
dkeff_Manual_bac = closureanalysis.dKeffCalculation(kmax=dk_Manual / (1 - r),
kclose=kc_Manual,
kmin=dk_Manual * (r /
(1 - r)),
method='basic')
# 移动平均
dkeff_Manual_averaged1, dk_Manual_averaged1 = \
closureanalysis.DoubleDataSelectMovingAverage(data=dkeff_Manual_bac, reference=dk_Manual,
ratio=ratio, numofaverage=numofaverage)
_, a_Manual_averaged1 = \
def AlphaModifiedCalculate(alpha_fade_rate, alpha_amplitude, pmax,
stress_ratio, thickness, width, a_amplitude, a_list,
c_ca, m_ca, a_start, a_end, dadn_start):
# Modified Alpha模型计算函数
# 该函数通过由已知起点(通常为a_kc_max_cal）和终点（通常为a_retard_end）的裂纹长度值和裂纹扩展速率
# 采用直线拟合得到Kop的值，代入已知的Alpha模型参数值计算
# 得到该段裂纹闭合效应主导的裂纹扩展速率模型
# input parameters:
# alpha_fade_rate: 模型衰减率参数
# alpha_amplitude: 模型峰值参数，常取2/pi
# pmax, stress_ratio: 载荷峰值，应力比
# thickness, width: CT试件几何参数厚度和宽度
# a_amplitude: 模型起点a0
# a_list：要计算的裂纹长度值的数组
# c_ca, m_ca：该应力比下的Paris公式参数
# a_start, a_end: 要输出的裂纹长度起止点
# dadn_start: 输入a0对应的dadn速率，通过反转Paris公式计算其dkeff
# return parameters:
# dk: 输入的a_list计算对应的dk
# dkeff_alpha_e: 输入的a_list对应的alpha模型下的dkeff
# dadn_alpha_e: 输入的a_list由alpha模型计算得到的dadn
# alpha_e: a_list各值对应的alpha值
# betas：a_list各值对应的无量纲裂纹长度参数值
kmax = mts_analysis.DeltaKCalculating(b=thickness,
w=width,
a=a_list,
pmax=pmax,
pmin=0)
kmin = mts_analysis.DeltaKCalculating(b=thickness,
w=width,
a=a_list,
pmax=pmax * stress_ratio,
pmin=0)
dk = kmax - kmin
# 计算无量纲量
betas = (a_list - a_amplitude) / a_amplitude
# 计算系数alpha
alpha_e = []
for beta in betas:
if beta < 0:
alpha_e.append(2 / np.pi)
else:
alpha_e.append(alpha_amplitude * np.exp(-alpha_fade_rate * beta))
alpha_e = np.array(alpha_e)
# 计算Kop
dk_start = mts_analysis.DeltaKCalculating(b=thickness,
w=width,
a=a_start,
pmax=pmax,
pmin=pmax * stress_ratio)
dk_end = mts_analysis.DeltaKCalculating(b=thickness,
w=width,
a=a_end,
pmax=pmax,
pmin=pmax * stress_ratio)
dkeff_start = mts_analysis.ParisInverseCalculation(c=c_ca,
m=m_ca,
dadn=dadn_start)
print("The Effective SIF when beta=0:" + str(dkeff_start))
pi = np.pi
kop_start = pi / 2 * (dk_start / (1 - stress_ratio) - dkeff_start -
(1 - 2 / pi) * dk_start * stress_ratio /
(1 - stress_ratio))
print("The Open SIF when beta=0 based on Alpha Method:" + str(kop_start))
kop_end = dk_end * (stress_ratio / (1 - stress_ratio))
dk_fit = [dk_start[0], dk_end]
kop_fit = [kop_start[0], kop_end]
k_kopfit_cal, b_kopfit_cal = mixed_model.LogLinearFit(y=kop_fit, x=dk_fit)
kop_cal = mixed_model.LogLinearFittedCalculate(k=k_kopfit_cal,
b=b_kopfit_cal,
x=dk)
# 计算dKeff
dkeff_alpha_e = kmax - alpha_e * kop_cal - (1 - alpha_e) * kmin
# 计算dadn
dadn_alpha_e = mts_analysis.ParisCalculating(c=c_ca,
m=m_ca,
dk=dkeff_alpha_e)
return dk, dkeff_alpha_e, dadn_alpha_e, alpha_e, betas
def Alpha2(sequence,
stress_ratio,
error_ratio,
numofaverage,
a_range,
amplitude=0,
fade_rate=0,
fitting=0,
model='paris'):
# usage: 采用提出的Alpha方法先拟合出幅度系数M，再根据其计算dadn结果
# input parameter:
# sequence: 试件名（与MTS中一致，将直接读取文件）
# stress_ratio：实验应力比
# error_ratio：进行数据筛选的误差带半宽度，详细注释见函数DoubleDataSelectMovingAverage
# numofaverage：进行移动平均的数据个数，详细注释见函数DoubleDataSelectMovingAverage
# a_range：拟合的数据范围，格式为数组[a_begin, a_end]，a_begin推荐为dkeff_basic的谷值或dadn的谷值，
# a_end要注意截止在数据开始离散之前
# fade_rate：幂函数中的指数系数，直接指定，常见[5,8]
# amplitude: 幂函数中的幅度系数，可定2/pi
# 注：函数自动将对输入为0的项先拟合参数再进行计算，若均不为零则直接计算不进行拟合
# fitting: 若fitting为1，则输出拟合时对标的dkeff_experiment值，以用于计算lost
# model: 设定计算过程中采用的model，默认采用paris，可选walker
# return parameter：
# Ce1: 计算得到的幅度系数
# dk_selected_averaged2, dkeff_alpha_e, dadn_alpha_e：对应的裂纹扩展参数
# alpha_e：对应的参数alpha
# 数据读入
dadn_Manual, n_Manual, dk_Manual, a_Manual, kc_Manual = \
BasicDataDispose(sequence=sequence, r=stress_ratio)
if model == 'walker':
c_w, m_w, gamma = paris_and_walker.WalkerParameter(data=1)
else:
c_p, m_p = paris_and_walker.ParisParameter(r=stress_ratio)
# 移动平均
kc_Manual_averaged2, dk_Manual_averaged2 = \
DoubleDataSelectMovingAverage(data=kc_Manual, reference=dk_Manual,
ratio=error_ratio, numofaverage=numofaverage)
_, a_Manual_averaged2 = \
DoubleDataSelectMovingAverage(data=kc_Manual, reference=a_Manual,
ratio=error_ratio, numofaverage=numofaverage)
_, dadn_Manual_averaged2 = \
DoubleDataSelectMovingAverage(data=kc_Manual, reference=dadn_Manual,
ratio=error_ratio, numofaverage=numofaverage)
# 数据筛选a_range
dadn_selecting_average2, dk_selecting_averaged2, kc_selecting_averaged2, a_selecting_averaged2 = \
mts_analysis.FCGDataSelectByThreshold(dadn=dadn_Manual_averaged2, dk=dk_Manual_averaged2,
n=kc_Manual_averaged2, a=a_Manual_averaged2,
threshold=a_range[0], target='a', keepbigger=1)
dadn_selected_averaged2, dk_selected_averaged2, kc_selected_averaged2, a_selected_averaged2 = \
mts_analysis.FCGDataSelectByThreshold(dadn=dadn_selecting_average2, dk=dk_selecting_averaged2,
n=kc_selecting_averaged2, a=a_selecting_averaged2,
threshold=a_range[1], target='a', keepbigger=0)
# 拟合数据准备
kmin_selected_averaged2 = dk_selected_averaged2 * (
stress_ratio / (1 - stress_ratio)) # Kmin计算
kmax_selected_averaged2 = dk_selected_averaged2 * (1 / (1 - stress_ratio)
) # Kmax计算
if model == 'walker':
dkeff_experiment_averaged2 = (
(dadn_selected_averaged2 / c_w)**(1 / m_w)) / (
(1 - stress_ratio)**(gamma - 1))
else:
dkeff_experiment_averaged2 = (dadn_selected_averaged2 / c_p)**(
1 / m_p) # 拟合时的真值dkeff，由Paris给出
beta = (a_selected_averaged2 - a_range[0]) / a_range[0] # 裂纹长度无量纲量
# 拟合，得到幅度或衰减系数
if fade_rate != 0 and amplitude == 0:
def residual_alpha_e(p):
Ce = p
return dkeff_experiment_averaged2 - (
kmax_selected_averaged2 -
(Ce * np.exp(-fade_rate * beta)) * kc_selected_averaged2 -
(1 -
(Ce * np.exp(-fade_rate * beta))) * kmin_selected_averaged2)
k = opt.leastsq(residual_alpha_e, np.array([1]))
Ce1 = k[0]
elif amplitude != 0 and fade_rate == 0:
def residual_alpha_e(p):
n = p
return dkeff_experiment_averaged2 - (
kmax_selected_averaged2 -
(amplitude * np.exp(-n * beta)) * kc_selected_averaged2 -
(1 -
(amplitude * np.exp(-n * beta))) * kmin_selected_averaged2)
k = opt.leastsq(residual_alpha_e, np.array([1]))
fade_rate = k[0]
Ce1 = amplitude
elif amplitude != 0 and fade_rate != 0:
Ce1 = amplitude
elif amplitude == 0 and fade_rate == 0:
def residual_alpha_e(p):
Ce, n = p
return dkeff_experiment_averaged2 - (
kmax_selected_averaged2 -
(Ce * np.exp(-n * beta)) * kc_selected_averaged2 -
(1 - (Ce * np.exp(-n * beta))) * kmin_selected_averaged2)
k = opt.leastsq(residual_alpha_e, np.array([1, 1]))
Ce1, fade_rate = k[0]
# 计算参数alpha
alpha_e = Ce1 * np.exp(-fade_rate * beta)
print("alpha幂函数拟合:试件名:", sequence, "幅度:", Ce1, "衰减速率:", fade_rate)
# 计算dkeff_alpha和对应的dadn
dkeff_alpha_e = kmax_selected_averaged2 - alpha_e * kc_selected_averaged2 - (
1 - alpha_e) * kmin_selected_averaged2
if model == 'walker':
dadn_alpha_e = mts_analysis.WalkerCalculating(c0=c_w,
gamma=gamma,
m0=m_w,
r=stress_ratio,
dk=dkeff_alpha_e)
else:
dadn_alpha_e = mts_analysis.ParisCalculating(c=c_p,
m=m_p,
dk=dkeff_alpha_e)
if fitting:
return Ce1, fade_rate, dk_selected_averaged2, dkeff_alpha_e, dadn_alpha_e, alpha_e, dkeff_experiment_averaged2
else:
return Ce1, fade_rate, dk_selected_averaged2, dkeff_alpha_e, dadn_alpha_e, alpha_e
aol=specimen.a_ol_applied, rol=plz_ol, plasticzonefactor=plz_factor,
m1=m1_2, c=c_ca, m=m_ca, eta=0)
# 2/PI法:
# dkeff计算
dkeff_Manual_2pi = closureanalysis.dKeffCalculation(
kmax=specimen.dk / (1 - specimen.stress_ratio),
kclose=specimen.kc,
kmin=specimen.dk * (specimen.stress_ratio / (1 - specimen.stress_ratio)),
method='2/PI')
dkeff_2pi, dk_2pi = \
closureanalysis.DoubleDataSelectMovingAverage(data=dkeff_Manual_2pi, reference=specimen.dk,
ratio=0.2, numofaverage=7)
_, a_2pi = \
closureanalysis.DoubleDataSelectMovingAverage(data=dkeff_Manual_2pi, reference=specimen.a,
ratio=0.2, numofaverage=7)
dadn_2pi = mts_analysis.ParisCalculating(c=c_ca, m=m_ca, dk=dkeff_2pi)
# Try: mix try 1
# 采用logistic sigmoid函数分配两种
# logistic sigmoid单调递增，表征crack closure
sigmas = 1 / (1 + np.exp(-kappa * betas))
dadn_mixed_1 = dadn_wheeler * (1 - sigmas) + dadn_alpha_e * sigmas
# 绘图部分
# Plotting
plt.figure(num=1, figsize=(8, 6))
plt.scatter(specimen.dk, specimen.dadn, lw=1, marker='+', label='Experiment')
if moving_average:
plt.scatter(dk_ave, dadn_ave, lw=1, marker='*', label='Moving average')
plt.plot(dk_wheeler2,
dadn_wheeler2,
dadn_Manual2, n_Manual2, dk_Manual2, a_Manual2, _ = \
closureanalysis.BasicDataDispose(sequence=sequence[1], r=stress_ratio[1])
dadn_Manual3, n_Manual3, dk_Manual3, a_Manual3, _ = \
closureanalysis.BasicDataDispose(sequence=sequence[2], r=stress_ratio[2])
dadn_Manual4, n_Manual4, dk_Manual4, a_Manual4, _ = \
closureanalysis.BasicDataDispose(sequence=sequence[3], r=stress_ratio[3])
dadn_Manual5, n_Manual5, dk_Manual5, a_Manual5, _ = \
closureanalysis.BasicDataDispose(sequence=sequence[4], r=stress_ratio[4])
# CA曲线计算
dk_paris = np.linspace(15, 25, 9)
dadn_paris = mts_analysis.ParisCalculating(c=c_CA, m=m_CA, dk=dk_paris)
plt.figure(num=1, figsize=(10, 8))
plt.scatter(dk_Manual1, dadn_Manual1, lw=1, marker='+', label='CA')
plt.scatter(dk_Manual2, dadn_Manual2, lw=1, marker='*', label='OLR=1.5')
plt.scatter(dk_Manual3, dadn_Manual3, lw=1, marker='2', label='OLR=2.0')
#plt.scatter(dk_Manual4, dadn_Manual4, lw=1, marker='3', label='OLR=2.5')
#plt.scatter(dk_Manual5, dadn_Manual5, lw=1, marker='1', label='OLR=4.0')
plt.plot(dk_paris, dadn_paris, label='CA_Paris', color='black', linewidth=2)
plt.axis([
min(dk_Manual1),
max(dk_Manual1),
min(dadn_Manual1),
max(dadn_Manual1) * 1.2
])
plt.yticks(np.linspace(min(dadn_Manual3) * 0.5, max(dadn_Manual1), 6))
c_p, m_p = paris_and_walker.ParisParameter(r=r)
# 数据读取
dadn_Manual, n_Manual, dk_Manual, a_Manual, kc_Manual = closureanalysis.BasicDataDispose(sequence=sequence[0], r=r)
dkeff_Manual = closureanalysis.dKeffCalculation(kmax=dk_Manual/(1-r), kclose=kc_Manual, kmin=dk_Manual*(r/(1-r)),
method='basic')
# moving average
numofaverage = 7
ratio = 0.5
dadn_Manual_averaged, dk_Manual_averaged = \
closureanalysis.DoubleDataSelectMovingAverage(data=dadn_Manual, reference=dk_Manual,
ratio=ratio, numofaverage=numofaverage)
# 无高载Paris虚线
dadn_paris_Manual = mts_analysis.ParisCalculating(c=c_p, m=m_p, dk=dk_Manual)
# ploting
plt.figure(num=1, figsize=(10, 8))
plt.scatter(dk_Manual, dadn_Manual, label='$ExperimentData$', color='red', marker='.')
plt.scatter(dk_Manual_averaged, dadn_Manual_averaged, label='$MovingAverage$', color='blue', marker='.')
plt.plot(dk_Manual, dadn_paris_Manual, label='$Paris for CA$', color='black', linewidth=2)
plt.axis([min(dk_Manual) * 0.95, max(dk_Manual) * 1.05, min(dadn_Manual) * 0.95, max(dadn_Manual) * 1.05])
plt.xlabel("DeltaK Applied (MPa*m^0.5)")
plt.xscale('log')
plt.ylabel("da/dN (mm/cycle)")
plt.yscale('log')
plt.xticks(np.linspace(min(dk_Manual), max(dk_Manual), 6))
plt.title('da/dN - dK ' + sequence[0] + '(MTS Result)')
plt.legend()
plt.grid()
