An experimental investigation of mixed-mode fracture

In this paper, mixed-mode fracture is investigated experimentally. In the first part, critical conditions for initiation of crack growth are explored. The method of caustics was used in conjunction with a high speed video system to determine critical stress intensity factors at initiation of crack growth. It was found that the maximum tangential stress criterion originally proposed by Erdogan and Sih [1] was the best criterion in terms of predictive capability. Polymethylmethacrylate and Homalite-100 were used in the experiments and Homalite-100 was found to exhibit significant rate dependence. In the second part, crack growth initiated under mixed-mode loading is addressed. It is shown that subsequent slow crack growth in PMMA is under pure mode-I conditions.

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Résumé On étudie par voie expérimentale les ruptures selon un mode mixte. On explore, dans une première partie, les conditions d'amorçage de la croissance d'une fissure. En utilisant la méthode des caustiques en association avec un système vidéo à grande vitesse, on détermine les facteurs critiques d'intensité de contraintes correspondant à l'amorçage de la fissure. On trouve que le critère de contrainte maximum tangentielle, proposé à l'origine par Erdogan et Sih, est le meilleur en termes de capacité de prédiction. Pour les essais, on a utilisé du plyméthylméthacrylate et de l'Homalite-100, et on a trouvé que ce dernier matériau faisait état d'une sensibilité importante à la vitesse. La deuxième partie du travail est consacrée à la croissance d'une fissure sous un mode de sollicitations mixte. On montre que la propagation lente de la fissure dans le PMMA se produit sous des conditions de pur Mode I.

     

Experimental investigation of mixed-mode fracture behaviour of woven laminated composite

In this paper, the mixed-mode interlaminar fracture behaviour of woven carbon-epoxy composite was investigated based on experimental and numerical analyses. A modified version of Arcan specimen was employed to conduct a mixed mode fracture test using a special loading device. A full range of mixed-mode loading conditions including pure mode-I and pure mode-II loading were created and tested. This test method has a simple procedure, clamping/unclamping the specimens are easy to achieve and only one type of specimen is required to generate all loading conditions. Also, finite element analysis was carried out for different loading conditions in order to determine correction factors needed for fracture toughness calculations. Interlaminar fracture toughness was determined experimentally with the modified version of the Arcan specimen under different mixed-mode loading conditions. Results indicated that the interlaminar cracked specimen is tougher in shear loading condition and weaker in tensile loading condition. Response of woven carbon-epoxy composite was also investigated through several criteria and the best criterion was selected. The interlaminar fracture surfaces of the carbon-epoxy composite under different mixed-mode loading conditions are examined by scanning electron microscopy (SEM).     

Characterization of mixed-mode fracture based on a complementary analysis by means of full-field optical and finite element approaches

This paper focuses on the characterization of mixed-mode fracture parameters through use of two formalisms based on Crack Relative Displacement Factors and Stress Intensity Factors, respectively. The evaluation of Crack Relative Displacement Factors is based on a kinematic approach that integrates the experimental displacement field measured by a digital image correlation method. In parallel with this step, the stress intensity factor is calculated from a finite element analysis. The coupling between these two approaches allows for the identification of fracture parameters in terms of an energy release rate without any prior knowledge of material elastic properties. Depending on the mixed-mode configuration, the proportion of the energy release rate corresponding to opening and shear modes can be calculated. Moreover, the proposed formalism allows determining, in addition to fracture parameters, the local elastic properties in terms of reduced elastic compliance directly from the test sample. Experimental protocols are carried out using a Single-Edge notched specimen made from a rigid Polyvinyl Chloride polymer loaded at various mixed-mode ratio values.     

Measurement of mixed-mode fracture parameters near cracks in homogeneous and bimaterial beams

An investigation of deformation fields and evaluation of fracture parameters near mixed-mode cracks in homogeneous and bimaterial specimens under elastostatic conditions is undertaken. A modified edge notched flexural geometry is proposed for testing bimaterial interface fracture toughness. The ability of the specimen in providing a fairly wide range of mode mixities is demonstrated through direct optical measurements and a simple flexural analysis. A full field optical shearing interferometry called Coherent Gradient Sensing (CGS) is used to map crack tip deformations in real time. Experimental measurements and predictions based on beam theory are found to be in good agreement. Also, for a large stiffness mismatch bimaterial system, the interface crack initiation toughness is evaluated as a function of the crack tip mode mixity.     

A boundary element alternating method for two-dimensional mixed-mode fracture problems

A boundary element alternating method (BEAM) is presented for two dimensional fracture problems. An analytical solution for arbitrary polynomial normal and tangential pressure distributions applied to the crack faces of an embedded crack in an infinite plate is used as the fundamental solution in the alternating method. For the numerical part of the method the boundary element method is used. For problems of edge cracks a technique of utilizing finite elements with BEAM is presented to overcome the inherent singularity in boundary element stress calculation near the boundaries. Several computational aspects that make the algorithm efficient are presented. Finally the BEAM is applied to a variety of two-dimensional crack problems with different configurations and loadings to assess the validity of the method. The method gave accurate stress-intensity factors with minimal computing effort.     

An equivalent domain integral method for three-dimensional mixed-mode fracture problems

A general formulation of the equivalent domain integral (EDI) method for mixed-mode fracture problems in cracked solids is presented. The method is discussed in the context of a 3-D finite-element analysis. The J-integral consists of two parts: the volume integral of the crack front potential over a torus enclosing the crack front and the crack surface integral due to the crack front potential plus the crack-face loading. In mixed-mode crack problems the total J-integral is split into J_I, J_II, and J_III, representing the severity of the crack front in three modes of deformation. The direct and decomposition methods are used to separate the modes. These two methods were applied to several mixed-mode fracture problems in isotropic materials. Several pure and mixed-mode fracture problems were analyzed and results found to agree well with those available in the literature. The method lends itself to be used as a post-processing subroutine in a general purpose finite-element program.     

Application of the biaxial Iosipescu method to mixed-mode fracture of unidirectional composites

In this paper the biaxial Iosipescu test method has been used, employing specimens with a central precrack placed along the notch-root axis, to study the intralaminar failure properties of a unidirectional carbon/epoxy composite under mixed-mode (dominated by shear) loadings. A linear finite element analysis has been performed to determine the energy release rates and stress intensity factors for the central crack under various biaxial loading conditions. In addition, a series of simple and biaxial fracture experiments have been performed on the composite material. Numerical results indicate that the method is capable of generating a wide range of mixed-mode loading conditions at the crack tip for various loading angles and crack lengths. Using the numerical results, in conjunction with experimental data, the biaxial intralaminar failure process in the cracked Iosipescu specimens has been explained.     

Continuum shape sensitivity analysis of mixed-mode fracture using fractal finite element method

This paper presents a new fractal finite element based method for continuum-based shape sensitivity analysis for a crack in a homogeneous, isotropic, and two-dimensional linear-elastic body subject to mixed-mode (modes I and II) loading conditions. The method is based on the material derivative concept of continuum mechanics, and direct differentiation. Unlike virtual crack extension techniques, no mesh perturbation is needed in the proposed method to calculate the sensitivity of stress-intensity factors. Since the governing variational equation is differentiated prior to the process of discretization, the resulting sensitivity equations predicts the first-order sensitivity of J-integral or mode-I and mode-II stress-intensity factors, K_I and K_II, more efficiently and accurately than the finite-difference methods. Unlike the integral based methods such as J-integral or M-integral no special finite elements and post-processing are needed to determine the first-order sensitivity of J-integral or K_I and K_II. Also a parametric study is carried out to examine the effects of the similarity ratio, the number of transformation terms, and the integration order on the quality of the numerical solutions. Four numerical examples which include both mode-I and mixed-mode problems, are presented to calculate the first-order derivative of the J-integral or stress-intensity factors. The results show that first-order sensitivities of J-integral or stress-intensity factors obtained using the proposed method are in excellent agreement with the reference solutions obtained using the finite-difference method for the structural and crack geometries considered in this study.     

On mixed-mode fracture of PVC foam

This paper reports on mixed-mode fracture in rigid cellular PVC foam based on experimental and numerical analyses. Experiments were performed on sharp-cracked specimens using the compact-tension-shear (CTS) test loading device. Foams of three different densities were tested. The CTS specimen was, in association with a special loading device, an appropriate apparatus for experimental mixed-mode fracture analysis. Experimentally-obtained fracture toughness results show good consistency. K_IC fracture toughness was marginally different in different directions. The ratio K_{II C}/K_{I C} was found to be between 0.4 and 0.65 depending on the foam density. For mixed-mode loading, Richard's criterion – using experimentally obtained K_{I C} and K_{II C} – was the best in predicting accurately fracture locus and fracture angle. When no experimental data were used, the maximum hoop stress criterion predicted best kinking angle. The principal strain criterion predicted the best fracture locus. Fracture boundary curve and kinking angle were best predicted for low mode II contribution. This revised version was published online in August 2006 with corrections to the Cover Date.     

Photoelastic investigation of the double-torsion specimen

The stress distribution of the double-torsion fracture mechanics specimen geometry is presented using a photoelastic “frozen stress” technique. Isochromatic fringes of a plastic double-torsion specimen under load were photographed and analyzed in the top, middle and bottom planes parallel to the top surface. Principal stress directions for these planes are also given. The relative magnitudes of the principal stresses perpendicular to the crack plane at the crack tip, crack origin and a point midway between the origin and crack tip are shown.     

Numerical study of mixed-mode fracture in concrete

In the present paper, a finite element code based on the microplane model for concrete is used for the analysis of typical mixed-mode geometries: a Single-Edge-Notched beam, a Double-Edge-Notched specimen and a Dowel-Disk specimen. A local smeared fracture finite element analysis is carried out. As a regularization procedure, the crack band method is used. The principal objective of the study was to investigate whether the smeared fracture finite element code is able to predict mixed-mode fracture of concrete with no optimisation of the material model parameters. Comparison between experimental and numerical results shows that the used code predicts structural response and crack patterns realistically for all cases investigated. Moreover, it is shown that for most of the studied geometries a mixed-mode fracture mechanism dominates at crack initiation, however, with increase of the crack length mode-I fracture becomes dominant and the specimens finally failed in mode-I fracture.     

Parameters identification of polymer concrete using a fracture mechanics test method and full-field measurements

In the present work it is proposed an easy-to-implement alternative procedure to identify not only the fracture properties but also the mean elasticity modulus E and Poisson’s ratio ν of arbitrary polymer concretes. Only one test using a standard single-edge-cracked three-point bend specimen is necessary. Digital image correlation (DIC) method is used to obtain the full-field displacement close to the crack tip. The mean properties (E, ν) are determined by fitting analytical expressions for the displacement field to the experimental data. The adequacy of the proposed methodology is checked by comparing the material parameters obtained using the proposed procedure with the ones obtained through standard procedures.     

Photoelastic investigation of bolted joints in composites

In this paper, the methods of photo-orthotropic elasticity are applied to the study of bolted joints in composites. The photoelastic models are E-glass fibre-reinforced epoxy strips loaded through a cylindrical pin, simulating bolt loading without lateral pressure. A special loading arrangement is devised so that the photoelastic response around the hole is not obscured. Quasi-isotropic and unidirectionally-reinforced specimens are tested, with ratios of end distance to hole diameter varying from 2 to 6. Photoelastic isochromatic fringe patterns are presented along with the shear stress distribution for the quasi-isotropic models.     

Effect of bond angle on mixed-mode adhesive fracture

A maximum in mixed-mode adhesive fracture energy has been observed at bond angles of 45° using scarf-joint test specimens. It is shown here that by reducing the adherend surface roughness from 1.2m CLA roughness (milled surfaces) to 0.08m CLA roughness (polished surfaces) the fracture energy becomes a linear function of bond angle (no maximum at 45°) and there is an overall crease in fracture energy at all bond angles. These results are discussed in terms of crack initiation being focused into the interfacial region and a pinning of crack-tip shear displacements by the surface roughness of the milled adherends which does not occur for the polished adherends.     

Experimental and computational investigation of three-dimensional mixed-mode fatigue

Experimental and computational methods were developed to model three-dimensional (3-D) mixed-mode crack growth under fatigue loading with the objective of evaluating proposed 3-D fracture criteria. The experiments utilized 7075-T73 aluminium forgings cut into modified ASTM E740 surface crack specimens with pre-cracks orientated at angles of 30, 45 and 60° in separate tests. The progress of the evolving fatigue crack was monitored in real time using an automated visualization system. In addition, the amplitude of the loading was increased at prescribed intervals to mark the location of the 3-D crack front for post-test inspection. In order to evaluate proposed crack growth equations, computer simulations of the experiments were conducted using a 3-D fracture model based on the surface integral method. An automatic mesher advanced the crack front by adding a ring of elements consistent with local application of fracture criteria governing rate and direction of growth. Comparisons of the computational and experimental results showed that the best correlation was obtained when K _II and K _III were incorporated in the growth rate equations.     

Photoelastic analysis of practical mode I fracture test specimens

A photoelastic technique for the evaluation of the isochromatic fringe patterns of practical Mode I fracture test specimen is presented.The new procedure uncouples the expressions for the stress intensity factor $\text{K}$ and the non-singular stress term $\text{A}$ from the governing maximum shear expression by employing a line perpendicular to the crack-tip in a photoelastic specimen, (this line intersects the isochromatic fringes at the locus of points $\text{r}{}_{\mathrm{i}}$, $\text{θ}{}_{\mathrm{i}}\text{= π/2}$, $\text{i = 1,2,…, n}$, where $\text{n}$ is the maximum analizable fringe) in developing the least-squares technique employed in this research.The least-squares expressions developed required no assumption of initial values for the stress intensity factor $\text{K}$ and the non-singular stress term $\text{A}$. The accuracy of the approach is then demonstrated by obtaining the $\text{K}$ and $\text{A}$ values of some practical Mode I specimens under applied uniaxial and biaxial stresses.     

Quantitative fractography of mixed-mode fracture in an R-curve material

Mixed-mode fracture surfaces of an R-curve material were quantitatively assessed using fractography. The R-curve material chosen was a mica glass ceramic. Vickers indentation cracks of different sizes were introduced at the center of tensile surface of glass ceramic bars fractured in flexure. The bars were fractured in flexure by generating mixed-mode (I/II) loading conditions at crack tips by orienting indentation cracks at various angles with respect to the tensile axis. Quantitative fractography indicated that crack-to-mirror size ratios were a function of crack length and mode mixity. Stress intensity at branching for the mirror–hackle transition during mixed-mode (I/II) fracture condition was a constant and was less than the corresponding stress intensity at branching in mode I loading. An empirical relationship is derived for the effective geometric factors in mixed-mode fracture of ceramics from surface cracks in flexure.     

Comparison of mode-resolved fracture strength of silicon with mixed-mode failure of diamond crystals

Currently ab initio theory provides the ideal tensile and shear strength of the {111} cleavage plane in single-crystal silicon and diamond only for few selected planes and directions (‘geometries’). These values can be compared with the real strength of nano-, micro-, and single-crystalline devices to roughly judge their mechanical quality. A novel contact-free and notch-free optical laser method allows the measurement of the fracture strength with plane nonlinear surface acoustic waves (SAWs), providing a unique way to discriminate between tensile and shear stresses for well-defined crystallographic planes and directions in anisotropic materials. Calibration yields the critical fracture stress or strength for the geometries, which can be compared with theory. In the case of diamond mostly mechanistically unresolved mixed-mode failure has been studied for complex geometries. Nevertheless, the comparison of these critical failure stresses with the strength of the ideal lattice and the mode- and geometry-resolved fracture behavior of silicon provides new insight into the mechanical stability and failure behavior of diamond materials.     

3-D elastic-plastic investigation of fracture parameters in side-grooved compact specimen

This paper presents an analytical comparison of a standard and a side-grooved compact tension specimen. Both specimens were analyzed using 3-13 finite element techniques in the elastic regime as well as under large-scale yielding conditions. The standard specimen reveals large variations of both the crack opening displacement and the energy release rate along the crack front clearly indicating that the crack will tend to propagate in a tunneling mode. The side-grooved specimen, on the other hand, provides a much more uniform variation of both parameters thereby promoting both flat fracture and a uniform crack growth. The results clearly indicate that for ductile materials loaded well into the plastic range, a much more uniform fracture process can be obtained with the side-grooved specimen. We also show that the Merkle-Corten method of estimating theJ-integral from an experimentally obtained load versus load-line displacement record is in good agreement with the average energy release rate calculated by the virtual crack extension method.