# US 2009/0276166 A1 · Methods and systems to predict fatigue life in aluminum castings

> Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt

- Number: US 2009/0276166 A1
- Document ID: US20090276166A1
- Status: Published application
- Kind: A1
- Application number: 12/114,875
- Filed: 2008-05-05
- Published: 2009-11-05
- Earliest claimed: 2008-05-05
- Assignees: GM Global Technology Operations LLC
- Inventors: Qigui Wang; Peggy E. Jones
- Web page: https://patentgrep.com/patent/US20090276166A1

## CPC

- G06F 30/20: Design optimisation, verification or simulation (optimisation, verification or simulation of circuit designs G06F30/30)
- G01M 5/0033: {by determining damage, crack or wear}
- G06F 2111/08: Probabilistic or stochastic CAD
- G06F 2119/04: Ageing analysis or optimisation against ageing
- G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N)
- G01M: TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR

## Abstract

Methods and systems of predicting fatigue life in aluminum castings that combines extreme values of both casting flaws and microstructures with multiscale life models. The multiscale life models account for differing fatigue crack initiation based on the size scale of the defect and microstructure features, including provisions for generally millimeter scale casting flaws, generally micrometer scale second phase particles by cracking or debonding, or submicrometer scale dislocation interactions with precipitates which form persistent slip bands. In the presence of casting flaws, the fatigue initiation life is negligible and the total fatigue life is spent in propagation of a fatigue crack from such flaws. In the absence of casting flaws, however, the total fatigue life is spent in both crack initiation and propagation, except for the case where fatigue cracks initiate from large second phase particles in a coarse microstructure. The extreme values of casting flaws, second phase particles, mean free path through an aluminum matrix or grain sizes are obtained from extreme value statistics when two or three dimensional sizes of casting flaws and microstructure features are provided by either direct measurement or analytical prediction. The upper bound flaw or microstructure feature size is calculated by extreme value statistics.

## Claims

### Claim 1

A method of predicting fatigue life for an aluminum based casting where at least one fatigue crack initiation site is presumed or determined to be present therein, said method comprising:
using extreme value statistical methods to estimate an upper bound initiation site size expected to occur in the casting; and
calculating on a computer said fatigue life based on said initiation site size using multiscale fatigue equations wherein a choice of which of said multiscale fatigue equations is selected is based upon at least one of a predominant form of said upper bound initiation site and a mean free path through an aluminum matrix of said aluminum based casting, wherein said predominant form of said upper bound initiation site comprises at least one of a casting flaw, a second phase particle and a persistent slip band, wherein said calculating comprises:
using the equation
N=Ni+Np=NpC1σa−maeq−(m−2)/2
in situations where said upper bound initiation site predominantly comprises said casting flaw such that a maximum flaw size of said casting flaw is larger than a critical size, whereas in situations where said maximum flaw size is smaller than said critical size, using the equation
N=Ni+Np=Np=C2(εmaxσaσys−1)naeqq;
using the equation
N=Ni+Np=Np=C3(εmaxσaσys−1)ndeqq;
in situations where said upper bound initiation site predominantly comprises said second phase particle and where a mean free path through an aluminum matrix associated with transgranular crack propagation is present and evidence of at least one of cracking and debonding of said second phase particle is present or anticipated, whereas in situations where said mean free path through said aluminum matrix associated with intergranular crack propagation is present and evidence of at least one of cracking and debonding of said second phase particle is present or anticipated, using the equation
N=Ni+Np=C4(Δεeqp)−e(dg)f+C5σa−m(dg)−(m−2)/2; or
using the equation
N=Ni+Np=C6(Δεeqp)−e(λeq)f+C7(εmaxσaσys−1)n(λeq)q;
in situations where said upper bound initiation site predominantly comprises said persistent slip band and where a size of said persistent slip band is constrained by a mean free path through said aluminum matrix that is smaller than a grain size is present and evidence of at least one of cracking and debonding of said second phase particle is not present or anticipated, whereas in situations where said initiation site predominantly comprises said persistent slip band and where a size of said persistent slip band is unconstrained by a mean free path through the aluminum matrix that is smaller than a grain size is present and evidence of at least one of cracking and debonding of said second phase particle is not present or anticipated, using the equation
N=Ni+Np=C8(Δεeqp)−e(dg)f+C9σa−m(dg)−(m−2)/2,
wherein C1 through C9, m, n, e, f and q are constants, σa is a stress amplitude, σys is a yield strength, εmax is a maximum total strain during loading cycle, εmax is maximum total strain during loading cycle, aeq is an equivalent initial crack-like defect size, deq is an equivalent initial crack-like second phase particle size, λeq is an equivalent mean free path through said aluminum matrix, Δεeq p is a local equivalent plastic strain and d8 is equivalent grain size.

### Claim at position 2

2-4. (canceled)

### Claim 5 (depends on 1)

The method of claim 1, wherein said critical size to distinguish between small and long crack behavior is determined for a particular alloy and microstructure by estimating a boundary therebetween as a function of at least one of a long crack growth threshold, fatigue strength and a geometric factor.

### Claim 6 (depends on 1)

The method of claim 1, wherein at least one fatigue crack initiation site is determined by at least one of direct measurement and analytical prediction.

### Claim 7 (depends on 6)

The method of claim 6, wherein said analytical prediction comprises computational simulation and modeling.

### Claim 8 (depends on 6)

The method of claim 6, wherein said direct measurement comprises at least one of X-ray computed tomography, single and serial sectioning metallography and fractography.

### Claim 9 (depends on 1)

The method of claim 1, wherein said extreme value statistics are used in conjunction with at least one of 2D metallographic techniques, fractographic techniques, X-ray computed tomography and computational simulation and modelling to estimate values of casting flaw and microstructure feature populations.

### Claim 10 (depends on 1)

The method of claim 1, wherein said extreme value statistics use a cumulative distribution function to provide upper bound flaw and feature size estimates.

### Claim 11 (depends on 10)

The method of claim 10, wherein said cumulative distribution function is represented by the equation
F

(
x
)
=
exp
(
-
exp
(
-
x
-
λ
δ
)
)
where x is a characteristic parameter of at least one of flaws and microstructural features, and where λ and δ are extreme value statistics location and scale parameters, respectively.

### Claim 12 (depends on 1)

The method of claim 1, wherein criterion for estimating the cracking or debonding of second phase particles is according to the equation
σp=4φβαtμmγmax*
where σp is fracture strength of second phase particle, γmax* is the critical maximum local shear strain, below which fatigue crack initiates by debonding, α is the particle aspect ratio, t is a constant between 0 and 1, φ is an “accommodation factor” equal to the elastic strain in the particle divided by the plastic strain in the matrix and depends on the morphology of particles and the slip system of the matrix, and is equal to 0.393 for spheres and 0.75 for plates in a matrix deforming by multiple slip, β is the modulus correction factor to account for elastic inhomogeneity and μm is the shear modulus of the aluminum matrix.

### Claim 13

An article of manufacture comprising a computer usable medium having computer readable program code embodied therein for predicting fatigue life in an aluminum casting, said computer readable program code in said article of manufacture comprising:
computer readable program code portion for causing a computer to determine which of a casting flaw, second phase particle and persistent slip band predominates as a cause of fatigue failure;
computer readable program code portion for causing the computer to calculate a predicted fatigue life based on extreme value statistics and a multiscale fatigue algorithm the latter of which is based on which of said predominant cause of fatigue failure is determined, wherein said multiscale fatigue life algorithm is configured such that in situations where fatigue behavior of the casting is dominated by said casting flaw, said multiscale fatigue life algorithm uses the equation
N=Ni+Np=Np=C1σa−maeq−(m−2)/2
in situations where a maximum flaw size in the casting is larger than a critical size, whereas in situations where said maximum flaw size is smaller than a critical size, said multiscale fatigue life algorithm uses the equation
N=Ni+Np=Np=C2(εmaxσaσys−1)naeqq;
wherein said multiscale fatigue life algorithm is configured such that in situations where fatigue behavior of the casting is dominated by at least one of said second phase particle and where a mean free path through an aluminum matrix associated with transgranular crack propagation is present and evidence of at least one of cracking and debonding of said second phase particle is present or anticipated, said multiscale fatigue life algorithm uses the equation
N=Ni+Np=Np=C3(εmaxσaσys−1)ndeqq;
whereas in situations where said mean free path through said aluminum matrix associated with intergranular crack propagation is present and evidence of at least one of cracking and debonding of said second phase particle is present or anticipated, said multiscale fatigue life algorithm uses the equation
N=Ni+Np=C6(Δεeqp)−e(dg)f+C5σa−m(dg)−(m−2)/2;
wherein said multiscale fatigue life algorithm is configured such that in situations where fatigue behavior of the casting is dominated by at least one said persistent slip band and where said persistent slip band size is constrained by a mean free path through said aluminum matrix that is smaller than a grain size is present and evidence of at least one of cracking and debonding of said second phase particle is neither present nor anticipated, said multiscale fatigue life algorithm uses the equation
N=Ni+Np=C6(Δεeqp)−e(λeq)f+C7)εmaxσaσys−1)n(λeq)q,
whereas in situations where said initiation site predominantly comprises said persistent slip band unconstrained by a mean free path through said aluminum matrix smaller than the grain size is present is present and evidence of at least one of cracking and debonding of said second phase particle is neither present nor anticipated, said multiscale fatigue life algorithm uses the equation
N=Ni+Np=C8(Δεeqp)−e(dg)f+C9σa−m(dg)−(m−2)/2,
wherein C1 through C9, m, n, e, f and q are constants, σa is a stress amplitude, σys is a yield strength, εmax is a maximum total strain during loading cycle, εmax is maximum total strain during loading cycle, aeq is an equivalent initial crack-like defect size, deq is an equivalent initial crack-like second phase particle size, λeq is an equivalent mean free path through said aluminum matrix, Δεeqp is a local equivalent plastic strain and d8 is equivalent grain size; and
computer readable program code portion configured to output results calculated by at least one of said equations to at least one of a machine-readable format and a human-readable format.

### Claim 14

(canceled)

### Claim 15 (depends on 13)

The article of manufacture of claim 13, wherein said determining which of a casting flaw, second phase particle and persistent slip band predominates as a cause of fatigue failure comprises at least one of direct measurement and analytical prediction.

### Claim 16 (depends on 13)

The article of manufacture of claim 13, wherein said critical size to distinguish between small and long crack behavior is determined for a particular alloy and microstructure by estimating a boundary therebetween as a function of at least one of a long crack growth threshold, fatigue strength and a geometric factor.

### Claim 17

A machine for predicting fatigue life in aluminum castings, said machine comprising:
a device configured to acquire at least one of measured or predicted sample defect information; and
a computing member configured to accept fatigue property data gathered from said device and further configured to calculate fatigue properties of the casting in accordance to instructions provided by a computer-readable program, said program comprising:
a code portion for causing said computing member to determine which of a casting flaw, second phase particle and persistent slip band predominates as a cause of fatigue failure;
a code portion for causing said computing member to calculate a predicted fatigue life by using extreme value statistical methods to estimate an upper bound initiation site size expected to occur in the casting and multiscale fatigue equations where at least one of said multiscale fatigue equations is selected based upon which of said casting flaw, second phase particle and persistent slip band predominates,
wherein situations where fatigue behavior of the casting is dominated by the casting flaw, said code portion uses the equation
N=Ni+Np=NpC1σa−maeq−(m−2)/2
in situations where a maximum flaw size in the casting is larger than a critical size, whereas in situations where said maximum flaw size is smaller than a critical size, using the equation
N=Ni+Np=Np=C2(εmaxσaσys−1)naeqq;
wherein situations where fatigue behavior of the casting is dominated by at least one second phase particle and where a mean free path through an aluminum matrix associated with transgranular crack propagation is present and evidence of at least one of cracking and debonding of said second phase particle is present or anticipated, said code uses the equation
N=Ni+Np=Np=C3(εmaxσaσys−1)ndeqq,
whereas in situations where said mean free path through an aluminum matrix associated with intergranular crack propagation is present and evidence of at least one of cracking and debonding of said second phase particle is present or anticipated, by using the equation
N=Ni+Np=C4(Δεeqp)−e(dg)f+C5σa−m(dg)−(m−2)/2; and
wherein situations where fatigue behavior of the casting is dominated by persistent slip bands and where said persistent slip band size is constrained by a mean free path through said aluminum matrix that is smaller than a grain size is present and evidence of at least one of cracking and debonding of second phase particles is neither present nor anticipated, said code uses the equation
N=Ni+Np=C6(Δεeqp)−e(λeq)f+C7(εmaxσaσys−1)n(λeq)q,
whereas in situations where said initiation site predominantly comprises said persistent slip band unconstrained by a mean free path through said aluminum matrix that is smaller than a grain size is present and evidence of at least one of cracking and debonding of second phase particles is neither present nor anticipated, using the equation
N=Ni+Np=C8(Δεeqp)−e(dg)f+C9σa−m(dg)−(m−2)/2,
wherein C1 through C9, m, n, e, f and q are constants, σa is a stress amplitude, σys is a yield strength, εmax is a maximum total strain during loading cycle, εmax is maximum total strain during loading cycle, aeq is an equivalent initial crack-like defect size, deq is an equivalent initial crack-like second phase particle size, λeq is an equivalent mean free path through said aluminum matrix, Δεeqp is a local equivalent plastic strain and dg is equivalent grain size.

### Claim 18

(canceled)

### Claim 19 (depends on 17)

The machine of claim 17, further comprising a code portion of said program configured to output results calculated by at least one of said equations to at least one of a machine readable format and a human readable format.

### Claim 20 (depends on 17)

The machine of claim 17, wherein said critical size to distinguish between small and long crack behavior is determined for a particular alloy and microstructure by estimating a boundary therebetween as a function of at least one of a long crack growth threshold, fatigue strength and a geometric factor.

### Claim 21 (depends on 13)

The article of manufacture of claim 13, wherein said extreme value statistics use a cumulative distribution function to provide upper bound flaw and feature size estimates.

### Claim 22 (depends on 21)

The article of manufacture of claim 21, wherein said cumulative distribution function is represented by the equation
F

(
x
)
=
exp

(
-
exp

(
-
x
-
λ
δ
)
)
where x is a characteristic parameter of at least one of flaws and microstructural features, and where λ and δ are extreme value statistics location and scale parameters, respectively.

### Claim 23 (depends on 13)

The article of manufacture of claim 13, wherein criterion for estimating the cracking or debonding of second phase particles is according to the equation
σp=4φβαtμmγmax*
where σp is fracture strength of second phase particle, γmax* is the critical maximum local shear strain, below which fatigue crack initiates by debonding, α is the particle aspect ratio, t is a constant between 0 and 1, φ is an “accommodation factor” equal to the elastic strain in the particle divided by the plastic strain in the matrix and depends on the morphology of particles and the slip system of the matrix, and is equal to 0.393 for spheres and 0.75 for plates in a matrix deforming by multiple slip, β is the modulus correction factor to account for elastic inhomogeneity and μm is the shear modulus of the aluminum matrix.

### Claim 24 (depends on 17)

The machine of claim 17, wherein said extreme value statistics use a cumulative distribution function to provide upper bound flaw and feature size estimates and wherein said cumulative distribution function is represented by the equation
F

(
x
)
=
exp

(
-
exp

(
-
x
-
λ
δ
)
)
where x is a characteristic parameter of at least one of flaws and microstructural features, and where λ and δ are extreme value statistics location and scale parameters, respectively.

### Claim 25 (depends on 17)

The machine of claim 17, wherein criterion for estimating the cracking or debonding of second phase particles is according to the equation
σp=4φβαtμmγmax*
where σp is fracture strength of second phase particle, γmax* is the critical maximum local shear strain, below which fatigue crack initiates by debonding, α is the particle aspect ratio, t is a constant between 0 and 1, φ is an “accommodation factor” equal to the elastic strain in the particle divided by the plastic strain in the matrix and depends on the morphology of particles and the slip system of the matrix, and is equal to 0.393 for spheres and 0.75 for plates in a matrix deforming by multiple slip, β is the modulus correction factor to account for elastic inhomogeneity and μm is the shear modulus of the aluminum matrix.