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A Novel Physics-Based Predictive Model for Small Fatigue Crack Growth with Microstructural Sensitivity in Cast Aluminum Alloys

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Abstract

A novel predictive model for microstructurally small fatigue crack growth rates was developed using a three-part methodology. First, a deterministic model was created to predict microstructurally small fatigue crack growth behavior from long fatigue crack growth data using considerations of crack tip plasticity. Subsequently, microstructural barrier characteristic spacing/strength were modeled to introduce characteristic acceleration and deceleration mechanisms of grain- and secondary phase-controlled cracks. Finally, the deterministic model was coupled with a Monte Carlo technique, and used to make predictions of lifetime distributions and S–N curves with material and component specificity. Simple, metallographically measured parameters are used to make predictions, and the model provides insight into their respective roles in controlling fatigue crack growth lifetimes, and enables design practice optimization. The model predicts that, for cast Al-Si-Mg alloy A356, increasing matrix strength, grain size, and secondary dendrite arm spacing enhances overall fatigue crack growth resistance. Comparisons are made to experimental data, and show that successful predictions are made.

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Abbreviations

A :

Power law pre-exponential constant

A grain :

Grain cross-sectional area

a :

Half crack length (internal crack) or crack length (surface crack)

a t :

Transition crack length from MSC to PSC

b :

Power law exponential constant

C m :

Empirical constant relating colony size to the barrier sensitivity exponent

c :

Crack length a plus the distance from the crack tip to the next barrier

da/dN :

Crack growth rate

(da/dN)MSC :

Microstructurally small crack growth rate

(da/dN)PSC :

Physically small crack growth rate

d n :

Proportionality constant between J and δ reflecting deviation from elastic behavior

E :

Elastic modulus

f 1 :

The fraction of dislocations on the slip band that participate in crack growth

f v :

Volume fraction of secondary phase particles

G :

Shear modulus

GS :

Grain size (μm)

i :

Index for the number of barriers traversed by the crack

ΔJ :

Strain energy release rate of the crack; work per unit fracture surface area

ΔJ elastic :

Elastic component of the strain energy release rate

ΔJ MSC :

Microstructurally small crack strain energy release rate

ΔJ plastic :

Plastic component of the strain energy release rate

ΔJPSC :

Physically small crack strain energy release rate

ΔJ total :

Total strain energy release rate; the sum of the elastic and plastic components

K max :

Maximum stress intensity factor (per cycle)

K norm :

Normalized stress intensity factor

ΔK I :

Mode I stress intensity amplitude

ΔK app :

Applied stress intensity amplitude

ΔK eff-ACR :

Effective, ACR-corrected stress intensity amplitude

ΔK MSC :

Microstructurally small crack stress intensity amplitude

ΔK plastic :

Plasticity-induced stress intensity amplitude

ΔK PSC :

Physically small crack stress intensity amplitude

m :

Barrier sensitivity exponent

N :

Number of secondary dendrite arms per dendritic cell

N L :

Linear density of interdendritic particles

N c.p./cell :

Number of colony particles per cell

N c.p./junction :

Number of colony particles per junction

N i.p./cell :

Number of interdendritic particles per cell

N junction/cell :

Number of junctions per cell

N total/cell :

Total number of particles per cell

n :

Dimensionless ratio of crack length to crack length plus the distance from the crack tip to the next barrier (equal to a/c)

n ACR :

Kmax sensitivity exponent

\( n_{c}^{i} \) :

The critical value of n in the current zone at which slip initiates in the subsequent zone

\( n_{s}^{i} \) :

The critical value of n in the subsequent zone at which slip initiates

R :

Stress ratio

r :

Average radius of secondary phase particle

S :

Stress ahead of the plastic zone

s :

Coordinate system defined along Γ

T :

Traction vector along the outward normal of Γ

u :

Displacement vector

W :

Strain energy density

x :

Cartesian coordinate axis with origin at the crack tip, parallel to crack surfaces

y :

Cartesian coordinate axis with origin at the crack tip, perpendicular to crack surfaces

α :

The ratio of microstructurally small to physically small crack growth rate, including the barrier magnitude effect

Γ:

A contour surrounding the crack tip, evaluated counter-clockwise

δ cl :

Crack mouth opening displacement at the minimum load

δ i :

Initial crack mouth opening displacement prior to initiation from a starter notch

δ nc :

Crack mouth opening displacement at the opening load

Δδ elastic :

Elastic component of the crack tip opening displacement

Δδ plastic :

Plastic component of the crack tip opening displacement

Δδ total :

Total crack tip opening displacement; the sum of the elastic and plastic components

ζ :

Dimensionless coordinate system = x/c

\( \zeta_{0}^{i} \) :

The value of ζ at which slip initiates in zone i

κ :

Constant = 1 for screw dislocations and = 1 − ν for edge dislocations

ν :

Poisson’s ratio

Δσ app :

Far-field applied stress amplitude

σ ys :

Matrix yield strength

τ :

Resolved shear stress on the plane of crack growth

φ :

Plastic displacement along the slip band

φ MSC :

Plastic displacement along the slip band attributed to the microstructurally small crack

φ PSC :

Plastic displacement along the slip band attributed to the physically small crack

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Acknowledgments

This work was supported by the National Science Foundation (Grant Number 1151588) and the members of the Integrative Materials Design Center (iMdc) at Worcester Polytechnic Institute.

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Authors and Affiliations

  1. Worcester Polytechnic Institute, Integrative Materials Design Center, Worcester, MA, 01069, USA

    Anthony G. Spangenberger & Diana A. Lados

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  1. Anthony G. Spangenberger
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  2. Diana A. Lados
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Correspondence to Anthony G. Spangenberger.

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Manuscript submitted March 5, 2019.

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Spangenberger, A.G., Lados, D.A. A Novel Physics-Based Predictive Model for Small Fatigue Crack Growth with Microstructural Sensitivity in Cast Aluminum Alloys. Metall Mater Trans A 50, 4364–4377 (2019). https://doi.org/10.1007/s11661-019-05349-z

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