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Research Papers

Scaling of Strength of Metal-Composite Joints—Part II: Interface Fracture Analysis

[+] Author and Article Information
Jia-Liang Le

Department of Civil and Environmental Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208jialiang-le@northwestern.edu

Zdeněk P. Bažant1

Departments of Civil Engineering and Materials Science, Northwestern University, 2145 Sheridan Road, CEE/A135, Evanston, IL 60208z-bazant@northwestern.edu

Qiang Yu

Department of Civil and Environmental Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208 qiangyu@northwestern.edu

1

Corresponding author.

J. Appl. Mech 77(1), 011012 (Oct 01, 2009) (7 pages) doi:10.1115/1.3172152 History: Received October 29, 2008; Revised April 13, 2009; Published October 01, 2009

The effect of the size of hybrid metal-composite joint on its nominal strength, experimentally demonstrated in the preceding paper (part I), is modeled mathematically. Fracture initiation from a reentrant corner at the interface of a metallic bar and a fiber composite laminate sheet is analyzed. The fracture process zone (or cohesive zone) at the corner is approximated as an equivalent sharp crack according to the linear elastic fracture mechanics (LEFM). The asymptotic singular stress and displacement fields surrounding the corner tip and the tip of an interface crack emanating from the corner tip are calculated by means of complex potentials. The singularity exponents of both fields are generally complex. Since the real part of the stress singularity exponent for the corner tip is not 12, as required for finiteness of the energy flux into the tip, the interface crack propagation criterion is based on the singular field of the interface crack considered to be embedded in a more remote singular near-tip field of the corner from which, in turn, the boundaries are remote. The large-size asymptotic size effect on the nominal strength of the hybrid joint is derived from the LEFM considering the interface crack length to be much smaller than the structure size. The deviation from LEFM due to finiteness of the interface crack length, along with the small-size asymptotic condition of quasiplastic strength, allows an approximate general size effect law for hybrid joints to be derived via asymptotic matching. This law fits closely the experimental results reported in the preceding paper. Numerical validation according to the cohesive crack model is relegated to a forthcoming paper.

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Figures

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Figure 1

Geometry of double-lap hybrid joint

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Figure 2

Geometry of bimaterial wedge

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Figure 7

Normal and shear stress along the interface: (a) left corner and (b) right corner

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Figure 8

Energy release rate at the hypothetical interfacial crack tip

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Figure 3

Exponent of displacement singularity of hybrid joint: (a) test series I and II and (b) test series III

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Figure 4

Interfacial crack embedded in the singular near-tip field of corner

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Figure 5

General geometry of hybrid joint with varying joint angle

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Figure 6

(a) Finite element model of hybrid joint and (b) finite element model of ancillary boundary layer problem

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