General size effect on strength of bimaterial quasibrittle structures

Le, Jialing

doi:10.1007/s10704-011-9653-3

Cited by 10 publications

(7 citation statements)

References 35 publications

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“…::Þ ð1Þ where k is the generalized stress intensity factor of a notch of bi-materials and F is the applied load, k c the critical generalized stress intensity factor or fracture toughness for a specific notch, which is a function of the notch angle b, tensile and shear strengths r c ; s c , mode I fracture toughness G Ic , and mode-mixity u and other parameters. Recently, Le [15] found that a size effect exists for the strong stress singularity at concave bi-material notches like the ones used in the current investigation. The strong stress singularity was calculated in our previous work [31].…”

Section: Introductionmentioning

confidence: 75%

An experimental study on the crack initiation from notches connected to interfaces of bonded bi-materials

Krishnan

2013

Engineering Fracture Mechanics

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Section: Introductionmentioning

confidence: 75%

An experimental study on the crack initiation from notches connected to interfaces of bonded bi-materials

Krishnan

2013

Engineering Fracture Mechanics

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“…(1) the peak load is reached when the stress intensity factor reaches a critical value (Carpinteri 1987;Dunn et al 1996;Gomez and Elices 2003), (2) the peak load is attained when the stress at a certain distance c f from the notch tip reaches the material tensile strength (Ritchie et al 1973;Ba zant and Yu 2006), and (3) the peak load is realized when the energy release rate of an equivalent crack that represents the FPZ reaches a critical value, i.e., the fracture energy (Le et al 2010;Le 2011). These criteria are all cast in the framework of linear elastic fracture mechanics, which can be used to derive the large-size asymptote of the size effect.…”

Section: Case Of Strong Stress Singularitymentioning

confidence: 99%

“…For Mode-I loading, all three criteria essentially yield the same form of the power-law size effect. Among these criteria, the second criterion is relatively straightforward to use, because the first criterion adopts a geometrydependent critical stress intensity factor, which needs to be measured for every notch angle (Ba zant and Yu 2006), and the third criterion requires determination of the energy release at the tip of an equivalent crack through the solution of an ancillary boundary value problem (Leguillon 2002;Le et al 2010;Le 2011).…”

Section: Case Of Strong Stress Singularitymentioning

confidence: 99%

Effect of Stress Singularity Magnitude on Scaling of Strength of Quasi-Brittle Structures

Pieuchot

Ballarini

2014

J. Eng. Mech.

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Engineering structures are often designed to have complex geometries, which could introduce stress singularities that are weaker than the conventional 21=2 crack-tip singularity. Extrapolating the results of small-scale laboratory tests to predict the response of a full-scale structure comprised of quasi-brittle materials requires an understanding of how the weak stress singularities modify the classical energetic and statistical scaling theories of quasi-brittle fracture. Through a theoretical and numerical study, a new scaling law for quasi-brittle fracture is derived, which explicitly relates the nominal structural strength to the structure size and the magnitude of the stress singularity. The theoretical analysis is based on a generalized weakest-link model that combines the energetic scaling of fracture with the finite weakest-link model. The model captures the transition from the energetic scaling to statistical scaling as the strength of the stress singularity diminishes. The new scaling law is in close agreement, for the entire range of stress singularities, with the size effect curves predicted through finite-element simulations of concrete beams containing an arbitrary-angle V-notch under Mode-I fracture.

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“…where £ = effective modulus of composites or steel, = geometry-dependent constant which can be determined by solving an auxiliary small-scale cracking problem [2,3,8,13,14]; Gf = fracture energy and Cf = length of the fully developed FPZ. Evidently, without knowing c/, the fracture energy Gf cannot be identified by fitting size effect data with Eq.…”

Section: Fig 4 Curves Of Load Versus Relative Displacement (Measuredmentioning

confidence: 99%

“…As such, the energetic argument of linear elastic fracture mechanics (LEFM) cannot directly be used to characterize the crack initiation from the comer. Rather, one must take into account the development of a finite fracture process zone (FPZ) at the inner comer, which can be quite large when dealing with a quasi-brittle material such as fiber composite [2,3]. For a propagating crack, the size of the FPZ is approximately constant, a material characteristic.…”

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confidence: 99%

Scaling of Strength of Metal-Composite Joints—Part III: Numerical Simulation

Bažant

2013

Journal of Applied Mechanics

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The size effect in the failure of a hybrid adhesive joint of a metal with a fiber-polymer composite, which has been experimentally demonstrated and analytically formulated in preceding two papers, is here investigated numerically. Cohesive finite elements with a mixed-mode ß-acture criterion are adopted to model the adhesive layer in the metal-composite interface. A linear tractionseparation softening law is assumed to describe the damage evolution at debonding in the adhesive layer. The results of simulations agree with the previously measured load-displacement curves of geometrically similar hybrid joints of various sizes, with the size ratio of 1:4:12. The effective size of the fracture process zone is identified from the numerically simulated cohesive stress profile at the peak load. The fracture energy previously identified analytically by fitting the e.xperimentally observed size effect cwves agrees well with the fracture energy of the cohesive crack model obtained numerically by optimal fitting of the test data. ] metal-composite joints. For a double-lap joint of steel and fiberpolymer composite analyzed and tested at Northwestern University (see Fig. 1 (test series 2 in Ref.[1])), the dominant stress singularity exponent was found to be A = -0.459 -I-0.06/ (/' = \f^) for the inner corners and / = -0.219 for the outer comers [2]. Since the stress singularity at the inner comer of the joint is stronger than at the outer one, a crack will emanate from the inner corner and propagate along the weakest plane in the bimaterial joint. This plane of propagation will lie either in the metal-composite interface or in the fiber composite.Although the stress singularity exponent at the inner comers is very close to the exponent of -1/2 at the crack tips, the analysis of fracture at the bimaterial corner is complicated by the fact that the elastic energy release rate corresponding to a singularity exponent > -1/2 is zero. As such, the energetic argument of linear elastic fracture mechanics (LEFM) cannot directly be used to characterize the crack initiation from the comer. Rather, one must take into account the development of a finite fracture process zone (FPZ) at the inner comer, which can be quite large when dealing with a quasi-brittle material such as fiber composite [2,3]. For a propagating crack, the size of the FPZ is approximately constant, a material characteristic. The consequence is a size effect on the strength of the metal-composite joints.The size dependence of the nominal strength of hybrid joints has been studied experimentally and theoretically in the preceding papers [1,2]. For example, when the strength values measured in test series 2 of Ref.[1] are plotted in a logarithmic scale, the nominal strengths of geometrically similar metal-c.omposite joints are seen to decrease with the joint size as seen in Fig. 2.It was found that the size dependence of joint strength can be expressed by a formula similar to the classical type 2 size effect law [4][5][6][7] that has been shown to apply to homogeneous qua...

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General size effect on strength of bimaterial quasibrittle structures

Cited by 10 publications

References 35 publications

An experimental study on the crack initiation from notches connected to interfaces of bonded bi-materials

An experimental study on the crack initiation from notches connected to interfaces of bonded bi-materials

Effect of Stress Singularity Magnitude on Scaling of Strength of Quasi-Brittle Structures

Scaling of Strength of Metal-Composite Joints—Part III: Numerical Simulation

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