Initiation and arrest of an interfacial crack in a four-point bend test

This paper describes a framework to study the initiation and arrest of an interfacial crack, using a combination of experiment and computation. We consider a test configuration widely used in the microelectronic industry: a sample of two substrates bonded by a stack of thin films, with a pre-crack in one of the substrates, perpendicularly impinging upon the films. When the sample is loaded to a critical level, the pre-crack initiates a new crack on one of the interfaces in the sample. The new crack often runs rapidly on the interface for a considerable length, and then arrests. We introduce a quantity, the initiation energy, to characterize the condition under which the pre-crack initiates the interfacial crack. The initiation energy is independent of the test configuration on the scale of the substrates, but changes greatly with the materials and stacking sequence of the films. We measure the initiation energy experimentally, interpret the data using mechanistic models, and use the initiation energy to predict the arrest crack length.     

Fracture toughness evaluation of a H.S.L.A. steel

The fracture toughness, J_Ic of a 3.5 Ni-Cr-Mo-V steel has been measured using the ASTM method. The results have been used to predict the stress intensity factor, K_Ic from the relationship between linear elastic and elastic-plastic fracture parameters. These predicted values were compared with K_Ic values obtained from empirical equations based on valid K_Ic tests, involving the Charpy upper shelf energy. It was found that the ASTM method for measuring J_Ic led to conservative estimates of K_Ic.     

Interaction effect crack–interfacial crack using finite element method

The interaction effect of an interfacial crack–microcrack modifies considerably the fracture behaviour of S45C/Si₃N₄ bimaterial. This work aims at studying the interaction effect of a crack located in one of the materials constituting the assembly near the interface, and that between an interfacial crack and a microcrack parallel to the interface by using the finite element method. The effect of transverse and longitudinal interaction distances between the interfacial crack and the microcrack are highlighted. The stress intensity factor of the interacting cracks and the bimaterial mechanical properties influence on the conditions of deviation and propagation of crack by interface and intercrack are examined.     

Fatigue crack propagation of through cracks in thin sheets under combined traction and bending stresses

ABSTRACT Fatigue crack propagation tests of through cracks in 3 mm thick aluminium alloy 6013‐T6 plates, under combined membrane and bending stresses were carried out. Five different values for the ratio of bending to membrane stresses, SB, were examined: 0, 0.55, 1.25, 1.8 and 2.23. Firstly, the results were elaborated by taking into account only the membrane stress and the front dimension of the crack for the evaluation of the stress intensity factor range. The results relevant to the lower SB values, evaluated in this mode, show good agreement with the results obtained when only the membrane stress was applied, while the results obtained at the higher SB values exhibit a remarkable increase in the crack propagation rate. The results were successively evaluated on the basis of tabular stress intensity factor solutions available in the literature; the agreement between the predicted and the experimental data occurs when mean values of stress intensity factor, rather than local values, were used at the back face of the plate, i.e., the face where the bending produces a compressive stress, to counteract the high gradient of stress intensity factor present in this area.     

Fracture toughness measurement of thin films on compliant substrate using controlled buckling test

Thin films and multilayered structures are increasingly used in the industry. One of the important mechanical properties of these thin layers is the fracture toughness, which may be quite different from the known value of the bulk sample due to microstructural difference. In the design towards device flexibility and scratch resistance, for example, fracture toughness is an important parameter of consideration. This work presents a testing scheme using controlled buckling experiment to determine the fracture toughness of brittle thin films prepared on compliant substrates. When the film is under tension, steady-state channelling cracks form in parallel to each other. Critical fracture strain can be calculated by the measuring the displacement of the buckled plate. The fracture toughness can then be obtained with the help of finite element calculation. When the substrate experiences plastic deformation, the energy release rate is increased by the degree of plasticity. Fracture toughness measurement of two types of thin film Cu-Sn intermetallic compounds has been given to illustrate the merits of such a test scheme.     

A non-contact, thermally-driven buckling delamination test to measure interfacial fracture toughness of thin film systems

Interfacial fracture toughness measurements of thin film-substrate systems are of importance in many applications. In the microelectronics industry, the interfacial adhesion between the dielectric-barrier-metal layers on a semiconductor chip is critical for chip reliability. In this paper, we propose a thermally-driven patterned buckling delamination test that does not use a pre-existing weak interface. The test relies on causing a patterned film to debond from its substrate by inducing a compressive stress due to heating of the film on a thick silicon substrate. The compressive stress causes the film to buckle and debond from the substrate. A model for the propagation of the buckling-induced debond is then developed to estimate interfacial fracture toughness. The efficacy of the thermally-driven buckling test is demonstrated on a model Al/SU8/Si film-substrate system wherein the Al film debonds along its interface to SU8. The interfacial toughness of the Al/SU8 interface is estimated using the proposed test and is compared to the toughness for the same system obtained using an alternative test with a weakened interface to validate the developed elastic-plastic model for buckling-induced debond propagation.     

Fracture toughness of hydroxide catalysis bonds between silicon carbide and Zerodur low thermal expansion glass-ceramic

In many optical and precision engineering applications, low thermal distortion materials need to be bonded together reliably. Since high temperature bonding process ultimately introduce stresses in the bond, rendering it dimensionally instable, room temperature or near room temperature processes are preferred. Low thermal distortion materials such as silicon carbide and low thermal expansion glass ceramics are bonded at room temperature using hydroxide catalysis bonding with a silicate bonding material. The bonding procedure is explained and fracture toughness results are presented for SiC–SiC, Zerodur–Zerodur and SiC–Zerodur bonds. A surface treatment technique for hydrating the SiC surface is presented, which eliminates the need for pre-oxidized SiC surfaces when using HCB bonding. The bonds between surface treated bare SiC surfaces and thermally oxidized SiC surfaces are found to have comparable fracture toughness.     

Investigation of mode III fracture toughness using an anti-clastic plate bending method

In this paper, results of a mode III (tearing mode) fracture toughness investigation with the method of anti-clastic plate bending (ACPB) or equivalently the plate twist method are reported. A testing device using the ACPB phenomenon was constructed and was used to determine the shear modulus of a number of foams and polymeric materials. In this work, potential applications of this method and the associated testing device were extended to the study of the mode III fracture toughness of various materials. The materials investigated included polymethylmethacrylate (PMMA), polycarbonate (PC), and foams consisting of polyvinylchloride (PVC), polyetherimide (PEI) and polymethacrylimide (PMI), polystyrene (PS-X) and laminated composites including carbon fiber reinforced plastic (CFRP), and glass fiber reinforced plastic (GFRP). Values for the compliance, energy release rate, and fracture toughness of these materials were obtained and the functional dependency of these quantities on the crack length was determined. This work shows that the ACPB method can provide a reliable and yet simple testing method not only for the determination of the shear properties of polymeric and laminated materials, but also for mode III fracture toughness investigations.     

Fracture toughness of ceramics and semi-brittle alloys using a miniaturized disk-bend test

∞ is the crack resistance at ”infinite” crack length. It is convincingly shown that this so-called R-curve equation correctly predicts K_∞, which is comparable to the conventionally measured Mode I plain-strain fracture toughness, K_Ic, of the same material. The fundamental constants in the fracture-mechanics-based equations are discussed, emphasizing the aspects pertinent to the small specimens used in the MDBT. Results are presented on 8 materials: ZnS, glass-ceramic, Si₃N₄, Ti₅Si₃, SiC, Ni₃Ge, NiAl and Ti-46.5A1-2.1Cr-3.0Nb-0.2W. All are brittle except for the latter two, which undergo slight plastic deformation before fracturing. The resulting values of K_∞ are in excellent agreement with published values derived from conventional measurements, providing considerable confidence in the method. where Q is a constant and K_∞ is the crack resistance at ”infinite” crack length. It is convincingly shown that this so-called R-curve equation correctly predicts K_∞, which is comparable to the conventionally measured Mode I plain-strain fracture toughness, K_Ic, of the same material. The fundamental constants in the fracture-mechanics-based equations are discussed, emphasizing the aspects pertinent to the small specimens used in the MDBT. Results are presented on 8 materials: ZnS, glass-ceramic, Si₃N₄, Ti₅Si₃, SiC, Ni₃Ge, NiAl and Ti-46.5A1-2.1Cr-3.0Nb-0.2W. All are brittle except for the latter two, which undergo slight plastic deformation before fracturing. The resulting values of K_∞ are in excellent agreement with published values derived from conventional measurements, providing considerable confidence in the method. Received: 13 October 1999 / Reviewed and accepted: 9 November 1999     

Mode III interlaminar fracture of carbon/epoxy laminates using a four-point bending plate test

A new four-point bending plate (4PBP) test was used for characterising the mode III interlaminar fracture of carbon/epoxy laminates. The specimen has a cross-ply lay-up and two edge delaminations whose propagation becomes visible at the edges. Although the test setup is very simple, determination of the mode III critical strain energy release rate G_IIIc requires finite element analyses (FEA). The virtual crack closure technique with an assumed initiation region was first proposed for computing G_IIIc. This scheme was subsequently validated by crack growth simulations with a cohesive zone model. The results showed an average G_IIIc = 1550 J/m², which is significantly higher than the G_IIIc = 850–1100 J/m² and G_IIc = 800 J/m² measured in previous studies.     

Examination of the Mode II fracture behaviour of wood with a short crack in an asymmetric four-point bending test

Asymmetric four-point bending tests of agathis specimens with a short crack along the neutral axis in a tangential–longitudinal system were conducted onto analyse the failure behaviour of wood with a short crack. The nominal shear strength and Mode II critical stress intensity factors of the specimens with various crack lengths were measured, and the influence of crack length on these properties was examined. The nominal shear strength of the cracked specimens was significantly lower than the strength of a crack-free specimen, even when the crack was extremely short. This finding suggests that the fracture mechanics theory is effective for analysing the failure behaviour of wood with a very short crack in this loading condition. However, the Mode II critical stress intensity factor still depends on the crack length. When the crack length was corrected with considering the formation of fracture process zone ahead of the crack tip, the critical intensity factor could be predicted effectively as well as the nominal shear strength.     

Fracture toughness of cast aluminium alloys

An investigation was carried out to evaluate the fracture toughness of cast aluminium alloys of different microstructural complexity, brought about by alloy constitution and cooling rate of castings. In all cases the three-point bend specimens, which had a thickness of 15 mm, did not provide valid plane — strain stress intensity factor values. The fracture susceptibility at a given stress level reckoned in terms of the conditional plane strain stress intensity factor (K _Q) was found to be lowest in aluminium-4.5% copper alloy castings and the susceptibility increased with increase in microstructural complexity. Casting cooling rate in these castings is likely to affect the damage potential of a given defect at yield stress to a greater extent than the fracture susceptibility at a given stress.     

Interaction of a wedge disclination dipole with interfacial cracks

The elastic interaction between a wedge disclination dipole and collinear interfacial cracks in bimaterials is investigated. The general solutions of complex potentials to this problem are presented by using complex potential theory. As illustrative examples, the closed-form solutions for a wedge disclination dipole interacting with a finite interfacial crack and a semi-infinite interfacial crack are obtained. The stress intensity factors at the tips of the crack and the force acting on the disclination dipole center are also given. The shield and anti-shield effect of the wedge disclination dipole upon the stress intensity factors is evaluated, and the equilibrium position of the disclination dipole is discussed for various crack geometries and material mismatch. The results indicate that the shielding or anti-shielding effect to the stress intensity factors increases acutely when the disclination dipole approaches the tip of the crack. If the center of the dipole is fixed, there always exists a critical value of angle of the dipole arm which the shielding or anti-shielding effect to the stress intensity factor is maximal. In addition, the length of the dipole arm and the material mismatch have significant influence on the stress intensity factors. The results also show that the interfacial crack always attracts the wedge disclination dipole and an equilibrium position of the disclination dipole may be available near the interface, which differs from the case of a perfect bonded interface, when the dipole approaches the surface of the crack from infinity. The present solutions contain a series of new and previously known results which can be shown to be special cases.     

Fracture toughness of steels with nickel content in respect of carbide morphology

Abstract

This paper is focused on the influence of Ni addition on the microstructure and fracture toughness of structural steels after tempering. Nickel is known to increase the resistance to cleavage fracture of steel and decrease a ductile–brittle transition temperature. The medium carbon, low alloy martensitic steels attain the best combination of properties in low tempered condition, with tempered martensite, retained austenite and transition carbides in the microstructure. In the present research, four model alloys of different Ni contents (from 0·35 to 4·00%) were used. All samples were in as quenched and tempered condition. Quenching was performed in oil at room temperature. After quenching, samples were tempered at 200°C for 2?h. An increase in nickel content in the investigated model structural steels causes a decrease in ε carbide volume fraction in their microstructure. Cementite nucleates independently in the boundaries of martensite laths and in the twin boundaries in the areas where the ε carbide has been dissolved. It was stated that stress intensity factor K_Ic significantly decreases in the case of the presence of dispersive elongated cementite precipitations at the boundaries of the prior austenite grains.     

Adhesion investigation of low-k films system using 4-point bending test

This research presents a simulation-based methodology to accurately predict interfacial adhesion behaviors of heterostructures. Validation of the proposed approach is achieved through comparison of 4-point bending test results on interfaces of multiple stacked low-k films with those of theoretical solutions from the finite element analysis. Impact induced by the compliance of 4-point bending test system can be neglected using the averaged energy release rate of various crack lengths in simulations. On the basis of precise predictions drawn from the considered analyses, uncertainty of experimental tests for the nano-scale fractured strength could be promptly observed and estimated.     

Fracture toughness of foams with tetrakaidecahedral unit cells using finite element based micromechanics

Fracture toughness of open-cell foams consisting of tetrakaidecahedral unit cells is predicted by simulating crack propagation using a finite element (FE) based micromechanical model. The inputs to the model are the geometric parameters required to model the repeating unit cell and tensile strength of the foam ligament or strut. Cracks are created by removing certain number of cells pertaining to a crack length. The FE model consists of a local micro-scale region surrounding the crack tip. For an assumed stress intensity factor, the displacements along the boundary of the local model are calculated based on linear elastic fracture mechanics for orthotropic materials. The stresses in the ligaments ahead of the crack tip calculated from this micro-model in conjunction with the tensile strength of the strut material are used to predict fracture toughness. A parametric study with different micro-model sizes and different crack lengths is performed to check for convergence of predicted Mode-I, Mode-II and mixed mode fracture toughness values. The effect of applying rotations as additional boundary conditions along with translational displacement boundary conditions on the predicted fracture toughness values is also studied.     

FRACTURE TOUGHNESS CALIBRATION OF THE Si3N4/Fe JOINT SYSTEM: A PARAMETRIC STUDY

Abstract— A fracture toughness calibration of the Si₃N₄/Fe joint system has been performed for various mixed-mode loading conditions and for different thicknesses of the metal interlayer. The asymmetric four-point-bend loading geometry was used. The values for the calibration function ( Y ) as well as the mode mixity (ψ)of the system increase on increasing the thickness of the metal. As the loading conditions change from mode II to mode I the dependence of both parameters on metal thickness is more intensive.     

Fracture mechanism of AZ31 magnesium alloy processed by equal channel angular pressing comparing three point bending test and tensile test

A commercial magnesium alloy, AZ31 in hot-rolled condition, has been processed by equal channel angular pressing (ECAP) to get microstructure modified. Uniaxial tensile tests were conducted along the rolling/extrusion direction for as-received AZ31 alloy and ECAPed AZ31 alloy. Then, three point bending fracture tests were conducted for specimens with a pre-crack perpendicular to the extruded direction. Digital image correlation (DIC) technique was adopted to determine the deformation field around the crack tip. The fracture surfaces of the failed specimens after tensile tests and fracture tests were observed by Scanning Electron Microscope (SEM). To explore the deformation mechanism, the microstructure and texture of different regions on the deformed specimens were examined through electron backscatter diffraction (EBSD). The results show ECAP process improves both the tensile elongation and fracture toughness of AZ31 alloy. Different from the slip dominated deformation mechanism in the tensile test, deformation twinning presents in the deformation zone adjacent to the crack tip in the three point bending fracture tests. The fracture surface is characterized by co-occurrence of dimple and cleavage features.     

Fatigue growth behavior for surface crack in welding joints under combined compressive and bending stresses

It has been demonstrated by experiments that crack can grow under cyclic compressive loading. However, it is difficult to observe and describe accurately by mathematical methods. In addition, cracks may close under compressive loading, which also increases the complexity of the problem. The fatigue growth behavior for surface cracks under biaxial loadings was studied by fatigue tests of HTS-A steel. According to experimental evidences, it is concluded that the transverse compressive stress not only changes the fracture morphology but also affect crack propagation life. Considering the influence of the compressive stress, this paper proposed an equivalent SIF and crack growth model subjected to compressive and bending stresses on the basis of McEvily formula. Finally, comparisons are made between prediction results and experimental data.     

Novel test method for accurate characterization of intralaminar fracture toughness in CFRP laminates

A novel initial crack insertion method, “intralaminar film insertion method”, was proposed to investigate the fracture toughness of unidirectional carbon fiber reinforced plastic (CFRP) laminates when the crack propagates inside the ply and not in the interlayer resin-rich area. Here, a release film was inserted inside a single lamina during the resin impregnation process of prepreg manufacturing. Mode I intralaminar fracture toughness tests were carried out for conventional CFRP laminates and interlayer toughened CFRP laminates. For comparison, two conventional methods were used to introduce initial cracks. One is the “interlaminar film method”, where a release film is inserted between two prepreg plies during the lay-up process. The other is the “machined slit method”, where a slit notch is machined in parallel to the layer of CFRP laminates. It was demonstrated that the proposed “intralaminar film method” can correctly evaluate the intralaminar fracture toughness of both conventional CFRP laminate and interlayer toughened CFRP laminate from the initial value to the propagation value. For this range, it was also found that the intralaminar fracture toughness of interlayer toughened CFRP laminate was the same as that of conventional CFRP laminate. Thus, the intralaminar fracture toughness was not influenced by interlayer toughening.