US2008078479A1PendingUtilityA1
Determining constitutive models for fracture prediction in ductile materials undergoing plastic deformation
Assignee: MASSACHUSETTS INST TECHNOLOGYPriority: Sep 29, 2006Filed: Sep 29, 2006Published: Apr 3, 2008
Est. expirySep 29, 2026(~0.2 yrs left)· nominal 20-yr term from priority
Inventors:Liang Xue
C21D 11/00C21D 6/02
44
PatentIndex Score
0
Cited by
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0
Claims
Abstract
Described are methods, systems, and apparatus, including computer program products for determining material constitutive relationships of fracture in a ductile material undergoing plastic deformation. A material pressure function is determined that describes dependence of a damage rule of at least a portion of the ductile material on pressure. A material azimuthal angle function is determined that describes dependence of the damage rule of the portion of the ductile material on principle stress. The damage rule of the portion of the ductile material is determined based on the material pressure function and the material azimuthal angle function. A weakening function of the portion of the ductile material is determined based on the damage rule. Material constitutive relationships of fracture in the portion of the ductile material are determined based on the weakening function and a matrix property of the ductile material.
Claims
exact text as granted — not AI-modified1 . A method of determining material constitutive relationships of fracture in a ductile material undergoing plastic deformation, the method comprising:
determining a material pressure function describing dependence of damage accumulation of at least a portion of the ductile material on pressure; determining a material azimuthal angle function describing dependence of damage accumulation of the portion of the ductile material on principle stress; determining a damage rule of the portion of the ductile material based on the material pressure function and the material azimuthal angle function; determining a weakening function of the portion of the ductile material based on the damage rule; and determining material constitutive relationships of fracture in the portion of the ductile material based on the weakening function and a matrix property of the ductile material.
2 . The method of claim 1 further comprising determining an initiation of fracture in the portion of the ductile material based on the weakening function and a matrix property of the ductile material.
3 . The method of claim 1 wherein the material pressure function includes a logarithmic function of pressure.
4 . The method of claim 3 wherein the material pressure function is:
μ
p
(
p
)
=
1
-
q
log
(
1
-
p
p
lim
)
.
5 . The method of claim 1 wherein when a relative ratio of principal stresses is between about 0 and about 0.5, the material azimuthal angle function is:
μ
θ
=
χ
2
-
χ
+
1
1
+
(
3
γ
-
2
)
χ
;
and when the relative ratio of principal deviatoric stresses is between about 0.5 and about 1, the material azimuthal angle function is:
μ
θ
=
χ
2
-
χ
+
1
1
+
(
3
γ
-
2
)
(
1
-
χ
)
.
6 . The method of claim 1 wherein the material azimuthal angle function is a material Lode angle function.
7 . The method of claim 6 wherein the material Lode angle function is:
μ
0
=
γ
+
(
1
-
γ
)
(
6
θ
L
π
)
k
.
8 . The method of claim 1 wherein the material azimuthal angle function is:
μ
0
=
1
-
(
1
-
γ
)
(
6
θ
π
)
k
for
0
≤
θ
≤
π
6
.
9 . The method of claim 1 wherein the material azimuthal angle function is:
μ
0
=
1
-
(
1
-
γ
)
(
6
π
/
3
-
θ
π
)
k
for
π
6
<
θ
≤
π
3
.
10 . The method of claim 1 wherein the damage rule is a function of the ratio of a plastic strain, ε p , to a fracture strain, ε f .
11 . The method of claim 10 wherein the damage rule is
D
=
(
ɛ
p
ɛ
f
)
m
.
12 . The method of claim 10 wherein the damage rule is
D
=
exp
[
λ
(
ɛ
p
ɛ
f
)
m
]
-
1
exp
[
λ
]
-
1
.
13 . The method of claim 1 wherein the damage rule is a function of the ratio of a plastic distortion ε d to a fracture strain ε p .
14 . The method of claim 13 wherein the damage rule is
D
=
(
ɛ
d
ɛ
p
)
m
.
15 . The method of claim 13 wherein the damage rule is
D
=
exp
[
λ
(
ɛ
p
ɛ
f
)
m
]
-
1
exp
[
λ
]
-
1
.
16 . The method of claim 1 wherein the weakening function is a linear function of the damage rule.
17 . The method of claim 1 wherein the weakening function is:
w ( D )=(1 −D β ) 1/η .
18 . The method of claim 17 wherein β is greater than one.
19 . The method of claim 17 wherein η is greater than one.
20 . The method of claim 1 wherein an equivalent stress is used to determine material constitutive relationships of fracture, the equivalent stress based on the weakening function and a matrix property of the ductile material.
21 . The method of claim 20 wherein the equivalent stress is:
σ = w ( D )σ M .
22 . A computer program product, tangibly embodied in an information carrier, the computer program product including instructions being operable to cause a data processing apparatus to:
determine a material pressure function describing dependence of a damage rule of at least a portion of a ductile material on pressure; determine a material azimuthal angle function describing dependence of the damage rule of the portion of the ductile material on principle stress; determine the damage rule of the portion of the ductile material based on the material pressure function and the material azimuthal angle function; determine a weakening function of the portion of the ductile material based on the damage rule; and determine material constitutive relationships of fracture in the portion of the ductile material based on the weakening function and a matrix property of the ductile material.
23 . The computer program product of claim 22 wherein the instructions are incorporated in at least one of: a software or hardware package.
24 . The computer program product of claim 23 wherein the software package is LS-DYNA or ABAQUS.
25 . A method of determining material constitutive relationships of damage accumulation in a ductile material undergoing plastic deformation, the method comprising:
determining a material pressure function describing dependence of a damage rule of at least a portion of the ductile material on pressure; determining a material azimuthal angle function describing dependence of the damage rule of the portion of the ductile material on principle stress; and determining a nonlinear damage accumulation rule for the portion of the ductile material based on the material pressure function and the material azimuthal angle function.
26 . The method of claim 25 further comprising:
determining a weakening function of the portion of the ductile material based on the nonlinear damage accumulation rule; and determining material constitutive relationships of fracture in the portion of the ductile material based on the weakening function and a matrix property of the ductile material.
27 . A method of determining damage accumulation characteristics of material constitutive relationships of fracture in a ductile material undergoing plastic deformation, the method comprising:
determining a material pressure function describing dependence of damage accumulation of at least a portion of the ductile material on pressure; determining a material azimuthal angle function describing dependence of damage accumulation of the portion of the ductile material on principle stress; determining a damage rule of the portion of the ductile material based on the material pressure function and the material azimuthal angle function; determining a damage accumulation in an integral form based on the material damage rule, the pressure function, and the material azimuthal angle function.
28 . The method of claim 27 further comprising:
determining a weakening function of the portion of the ductile material based on the nonlinear damage accumulation rule; and determining material constitutive relationships of fracture in the portion of the ductile material based on the weakening function and a matrix property of the ductile material.
29 . A method of determining material constitutive relationships of fracture in a ductile material undergoing plastic deformation, the method comprising:
means for determining a material pressure function describing dependence of damage accumulation of at least a portion of the ductile material on pressure; means for determining a material azimuthal angle function describing dependence of damage accumulation of the portion of the ductile material on principle stress; means for determining a damage rule of the portion of the ductile material based on the material pressure function and the material azimuthal angle function; means for determining a weakening function of the portion of the ductile material based on the damage rule; and means for determining material constitutive relationships of fracture in the portion of the ductile material based on the weakening function and a matrix property of the ductile material.
30 . A method of determining material constitutive relationships of fracture in a ductile material undergoing plastic deformation, the method comprising:
determining a material pressure function describing dependence of damage accumulation of at least a portion of the ductile material on pressure; determining a material azimuthal angle function describing dependence of damage accumulation of the portion of the ductile material on principle stress; determining a damage rule of the portion of the ductile material based on the material pressure function and the material azimuthal angle function; determining a weakening function of the portion of the ductile material based on the damage rule, wherein the weakening function is a function of damage accumulation and the rate of change of the weakening function with respect to damage accumulation is dependent on damage accumulation; and determining material constitutive relationships of fracture in the portion of the ductile material based on the weakening function and a matrix property of the ductile material.Join the waitlist — get patent alerts
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