Numerical and experimental investigation of mixed‐mode fracture parameters on silicon nitride using the Brazilian disc test

Engineering applications of ceramics can often involve mixed‐mode conditions involving both tensile and shear loading. Mixed‐mode fracture toughness parameters are evaluated for applicability to ceramics using the Brazilian disc test on silicon nitride. Semi‐elliptical centrally located surface flaws are induced on the disc specimens using Vickers indentation and compression loaded to fracture with varying levels of mode mixity. The disc specimens are modelled via 3D finite element analysis and all three modes of stress intensity factors computed along the crack front, at failure load. We present a numerical and experimental investigation of four widely used mixed‐mode fracture criteria and conclude that the critical strain energy release rate criterion is simple to implement and effective for silicon nitride under mixed‐mode conditions.     

Effect of thickness on fracture criterion in general yielding fracture mechanics

In this research work, the effect of thickness on fracture criterion is studied for extra deep drawn (EDD) steel sheets. Experimental results are generated on fracture toughness of EDD steel sheets using compact tension specimens and a ‘maximum load’ as a fracture criterion. Critical crack tip opening displacement (CTOD) is found with the help of three methods: plastic hinge model (PHM), crack flank opening angle (CFOA) and finite element model (FEM). The fracture toughness is found to increase with increase in thickness of specimens. The fracture behaviour exhibited characteristics of general yielding fracture mechanics.     

Effect of hardening models on different ductile fracture criteria in sheet metal forming

Prediction of the fracture is one of the challenging issues which gains attention in sheet metal forming as numerical analyses are being extensively used to simulate the process. To have better results in predicting the sheet metal fracture, appropriate ductile fracture criterion (DFC), yield criterion and hardening rule should be chosen. In this study, the effects of different hardening models namely isotropic, kinematic and combined hardening rules on the various uncoupled ductile fracture criteria are investigated using experimental and numerical methods. Five different ductile fracture criteria are implemented to a finite element code by the user subroutines. The criterion constants of DFCs are obtained by the related experimental tests. The in-plane principle strains obtained by the finite element analyses for different DFCs are compared with the experimental results. Also, the experimental results are used to evaluate the principle strain values calculated by the finite element analysis for different combinations of DFCs and hardening rules. It is shown that some DFCs give better predictions if the appropriate hardening model is employed.     

A finite fracture mechanics approach to structures with sharp V-notches

Criteria assuming that failure of quasi-brittle materials is affected by the stresses acting over a finite distance from the crack tip are widely used inside the scientific community. For instance, they have been applied to predict the failure load of specimens containing sharp V-notches, assuming as a critical parameter the average stress ahead the notch tip. However, this kind of approaches disregards energy balance considerations, which, as well known, are the basis of linear elastic fracture mechanics (LEFM). In order to overcome these drawbacks, the present paper uses a recently introduced finite fracture mechanics (FFM) criterion, i.e. a fracture criterion assuming that crack grows by finite steps. The length of this finite extension is determined by a condition of consistency of both energy and stress requirements; as a consequence, the crack advancement is not a material constant but a structural parameter. The criterion is applied to structures with sharp V-notches. The expression of the generalized fracture toughness, which is a function of material tensile strength, fracture toughness and notch opening angle, is given analytically. Finally, we provide comparisons with: (i) the experimental data we obtained from testing Polystyrene specimens under three point bending; (ii) some experimental data available in the literature. The agreement between theoretical predictions and experimental results is generally satisfactory and, for most of the cases analyzed, the FFM predictions are better than the ones provided by the simple average stress approach.     

Multiparametric sufficient criterion of quasi-brittle fracture for complicated stress state

Behaviour of an atomic structure in the vicinity of the crack tip is simulated. Buckling and postbuckling deformation of three- and four-atomic cells at generalized tension is studied. A discrete-integral fracture criterion is proposed for normal rupture cracks when stress fields have a singular component, vectors of fields of stresses and deformations being collinear. When formulating the proposed criterion, we used the new rank of solutions, which differ from solutions applied in formulating the classical sufficient fracture criterion, in conformity with Novozhilov’s hybrid model. The proposed criterion permits limiting passage to necessary criterion when energetic characteristics of postbuckling deformation of cells can be neglected within the limit. Values of critical loads obtained in conformity with the sufficient criterion essentially differ from those obtained in conformity with the necessary criterion.     

A numerical fracture analysis of indentation into thin hard films on soft substrates

In this paper, finite element simulations of spherical indentation of a thin hard film deposited on a soft substrate are carried out. The primary objective of this work is to understand the mechanics of fracture of the film due to formation of cylindrical or circumferential cracks extending inwards from the film surface. Also, the role of plastic yielding in the substrate on the above mechanics is studied. To this end, the plastic zone development in the substrate and its influence on the load versus indentation depth characteristics and the stress distribution in the film are first examined. Next, the energy release rate J associated with cylindrical cracks is computed. The variation of J with indentation depth and crack length is investigated. The results show that for cracks located near the indenter axis and at small indentation depth, J decreases over a range of crack lengths, which implies stability of crack growth. This regime vanishes as the location of the crack from the axis increases, particularly for a substrate with low yield strength. Finally, a method for combining experimental load versus indentation depth data with simulation results in order to obtain the fracture energy of the film is proposed.     

Numerical modelling of magnesium die-castings using stochastic fracture parameters

Quasi-static material tests using specimens cut from a generic cast component are performed to study the behaviour of the high-pressure die-cast magnesium alloy AM60 under different stress states. The experimental data set is applied to establish a validated probabilistic methodology for finite element modelling of thin-walled die-castings subjected to quasi-static loading. The test specimens are modelled in the explicit finite element (FE) code LS-DYNA using shell elements. The cast magnesium alloy AM60 is modelled using an elasto-plastic constitutive model including a high-exponent, isotropic yield criterion, the associated flow law and isotropic hardening. To simulate fracture, the Cockcroft-Latham fracture criterion is adopted, and the fracture parameter is chosen to follow a modified weakest-link Weibull distribution. Comparison between the experimental and predicted behaviour of the cast magnesium specimens gives very promising results.     

Application of an indentation method to the fracture mechanics study of a polycrystalline graphite

None of the conventional indentation techniques are applicable to carbon and graphite materials for determining fracture mechanics parameters because of the difficulty in introducing well-defined median/radial cracks. A novel indentation method is proposed in this work for fracture mechanics studies and then applied to a polycrystalline graphite fracture. The most prominent advantage of the indenter designed is that the residual stresses beneath the indentation impression, which prevail in conventional indentation methods (Knoop and Vickers indentations) and lead to crucial difficulties in fracture mechanics analysis, are negligibly small. This makes possible a quantitative study on the microstructural interaction between the indentation-induced micro-flaw and the natural intrinsic flaws of the material. The dependence of flexural strength of a polycrystalline graphite on the indentation-induced surface flaw size is also discussed by examining the microstructural scaling transition of fracture origin from the indentation-induced to the intrinsic flaws with diminishing indentation surface flaw. An important role of the Mrozowsky micro-crack system in the scaling transition is emphasized.     

Branching model for the fracture of fibre composites

Models of localized and delocalized fracture of fibre reinforced composite materials have been considered from the viewpoint of the theory of branching processes. The analysis has shown that, in spite of apparent differences, both types of models can be reduced to generally the same Markov chain. As a result, a new fracture criterion has been proposed that is valid for any model. The use of the new criterion allowed for the revelation of a new structural effect, i.e. the dependence of the fracture stress of the composite upon the size of the cross-section of the composite sample. In the case of a fracture of an infinitely large composite sample, the criterion yields the same fracture stress as calculated on the basis of earlier models. In the case of the fracture of a sample of a finite size, the predicted fracture stress is lower than calculated according to previous models. The effect can be explained as a non-linear fracture phenomenon arising out of the non-linear dependence of microfracture probabilities upon overstressing caused by other microfractures. The effect is essential for evaluating the strength of a structured composite with several levels of ordering and constriction elements of a small size.     

Meshfree simulations of thermo-mechanical ductile fracture

In this work, a meshfree method is used to simulate thermo-mechanical ductile fracture under finite deformation. A Galerkin meshfree formulation incorporating the Johnson-Cook damage model is implemented in numerical computations. We are interested in the simulation of thermo-mechanical effects on ductile fracture under large scale yielding. A rate form adiabatic split is proposed in the constitutive update. Meshfree techniques, such as the visibility criterion, are used to modify the particle connectivity based on evolving crack surface morphology. The numerical results have shown that the proposed meshfree algorithm works well, the meshfree crack adaptivity and re-interpolation procedure is versatile in numerical simulations, and it enables us to predict thermo-mechanical effects on ductile fracture.     

An experimental verification of nonlocal fracture criterion

By using a nonlocal field theory, Eringer et al. [6] obtained a finite solution for the stress at the tip of a sharp crack. This solution permitted the development of a nonlocal fracture criterion for crystalline materials that is given in terms of atomic distance and theoretical cohesive strength.

The nonlocal fracture criterion is generalized for application to real materials by the introduction of a characteristic dimension (a measure of the size of the internal structures). Particleboard, a wood-based composite with controllable internal characteristics (particle dimensions and amount of resin), is used to substantiate the nonlocal fracture criterion.     

On dual-parameter fracture criterion of welded joints

Based on the existed results of stress field solutions, in the present work a modified dual parameter JQ fracture criterion is proposed for plane strain state, and the criterion may be suitable to both homogeneous material and welded joint. Center cracked welded plate in plane strain condition is selected as a research object. Combined with finite element analysis, discussions are made on the engineering estimate and measurement of the various parameters. The engineering algorithm on the various factors in the fracture criterion is also proposed. Referring to the HRR results, it is indicated that the new criterion can describe stress field nature of homogeneous material and welded joint in plane strain state well. The availability of the new proposed criterion to the homogeneous material and welded joint is discussed. Thereafter, the difficulty of the single parameter J-integral can be overcome, when the modified J-integral parameter is used to describe the stress field intensity of plane strain and weld joint. Thus, the new criterion may be a good basis for engineering evaluation of fracture of welded structures.     

Evaluation of fracture toughness of cartilage by micropenetration

Failure properties of cartilage are important in injury repair and disease, but few methods exist for measuring these properties, especially in small animals. To meet this need, a new indentation/penetration method for measuring fracture toughness of cartilage is proposed. During indentation, a conical tip is displaced into the surface of the cartilage, causing first a non-penetrating indentation, and then a penetration into the tissue. The method assumes that tissue penetration occurs during periods of rapid work, which are identified from a curve of work rate vs. time. Total penetration depth is determined by summing the displacement during these periods. Fracture work is the work that occurs during rapid work, or penetration, and fracture toughness defined as the fracture work divided by one-half the penetrated surface area of the indenting tip. The method was validated by indentation testing of bovine cartilage. Penetrating indentations with a conical tip were performed in bovine patellar cartilage and depth of penetration and fracture toughness predicted. For comparison with the indentation data, depth of penetration was measured in histological sections. These measurements agreed well with the predicted depth. Predicted fracture toughness also agreed with values measured via a macroscopic test. This newly described method has promise as a general method for measuring fracture toughness in cartilage, particularly in small animals, since penetrating tips with small tip radius can be manufactured and penetration may be accomplished in cartilage of minimal thickness.     

Mixed-mode I/II wood fracture characterization using the mixed-mode bending test

In this work fracture characterization of wood under mixed-mode I/II loading is addressed. The mixed-mode bending test is used owing to its aptitude for easier alteration of mode ratio. Experimental tests were performed covering a wide range of mode ratios in order to obtain a mixed-mode fracture criterion for the maritime pine (Pinus pinaster Ait.) in the RL crack propagation system. A data reduction scheme based on beam theory and crack equivalent concept was used to overcome some difficulties inherent to the test. The method does not require crack length monitoring during propagation and provide an entire resistance curve allowing easier identification of the fracture energy. A numerical analysis using cohesive elements was also performed to validate the method. The linear energetic fracture criterion was proved to be the most adequate to describe the failure envelop of this wood species.     

Theoretical analysis of Hertzian contact fracture: Ring crack

The axisymmetric fracture behavior of brittle materials under an applied indentation force is investigated by considering the pile-up of Somigliana ring dislocations. For such a mixed-mode crack problem, the stress intensity factors (SIFs) and strain energy release rate are obtained by solving a system of Cauchy singular integral equations. The Auerbach range is extensively studied during the formation of a shallow ring crack. The Auerbach constant is also determined from the exact solutions, enabling the prediction of surface energy from Hertzian indentation tests. The obtained results can be used to extract the fracture parameters of brittle materials by using the indentation technique.     

Crack repair performance of piezoelectric actuator estimated by slope continuity and fracture mechanics

The active repair performance of the piezoelectric actuator for the cracked structure is studied in this paper. As an extension of the author’s previous study, this paper discusses a special repair case and new results by using two repair criteria: the slope continuity criterion and fracture mechanics criterion. Crack contact analyses and fracture mechanics in the crack tip field are considered in the plane strain finite element analyses. From numerical results, it is concluded that the fracture mechanics criterion is better for defining the repair voltage. The crack tip field and crack contact condition must be considered to obtain correct results. However, it is not a good idea for the active repair to use higher applied voltage on the piezoelectric actuator.     

On fracture testing of piezoelectric ceramics

Fracture tests carried out on unpoled and poled PZT-5H four-point bend specimens are presented in this paper. The crack faces were parallel to the poling direction. Both mechanical loads and electric fields were applied to the poled specimens. The experimental results were analyzed by means of the finite element method and a conservative M-integral including the crack face boundary conditions. Fracture tests on four-point bend PIC-151 specimens with the crack faces perpendicular to the poling directions were also analyzed here; the experimental results were taken from the literature. A mixed mode fracture criterion is proposed for piezoelectric ceramics. This criterion is based upon the energy release rate and two phase angles. This criterion was implemented with experimental results from the literature and from this investigation. Excellent agrement was found between the fracture curve and the experimental results of the specimens with the crack faces perpendicular to the poling direction. With some scatter, reasonable agreement was observed between the fracture curve and the experimental results of the specimens with crack faces parallel to the poling direction.     

Finite fracture mechanics: A coupled stress and energy failure criterion

The aim of the present paper is to introduce a new failure criterion in the framework of Finite Fracture Mechanics. Criteria assuming that failure of quasi-brittle materials is affected by stress or energy flux acting on a finite distance in front of the crack tip are widely used inside the scientific community. Generally, this distance is assumed to be small compared to a characteristic size of the structure, i.e. to any length describing the macroscale. A key point of the present paper is to analyse what happens if the smallness assumption does not hold true. The proposed approach relies on the assumption that the finite distance is not a material constant but a structural parameter. Its value is determined by a condition of consistency of both energetic and stress approaches. The model is general. In order to check its soundness, an application to the strength prediction for three point bending tests of various relative crack depths and of different sizes is performed. It is seen that, for the un-notched specimens, the present model predicts the same trend as the Multi-Fractal Scaling Law (MFSL). Finally, a comparison with experimental data available in the literature on high strength concrete three point bending specimens is performed, showing an excellent agreement. It is remarkable to observe that the method presented herein is able to provide the fracture toughness using test data from un-notched specimens, as long as the range of specimen sizes is broad enough.     

J integral as a fracture criterion of rubber-like materials using the intrinsic defect concept

Using the fracture mechanics framework, a fracture criterion based upon the intrinsic defect concept was developed to predict the failure of rubber parts under biaxial monotonic loading. This fracture criterion requires as input data the fracture toughness of the material in terms of critical value of the J integral, the constitutive law of the material and the breaking stretch of a smooth specimen under uniaxial tension. To develop this criterion a generalized expression of the J integral under biaxial loading is proposed on the basis of finite element calculations on a RVE containing a small circular defect. The estimated failure elongations were found in very nice agreement with experimental data on two kinds of rubber materials. Moreover, we have also shown that this criterion could be extended to the failure analysis of thermoplastic polymers.     

Linear electro-elastic fracture mechanics of piezoelectric materials

The concepts of linear elastic fracture mechanics, generalized to treat piezoelectric effects, are employed to study the influence of the electrical fields on the fracture behavior of piezoelectric materials. The method of distributed dislocations and electric dipoles, already existing in the literature, is used to calculate the electro-elastic fields and the energy-release rate for a finite crack embedded in an infinite piezoelectric medium which is subjected to both mechanical and electric loads. The energy-release rate expressions show that the electric fields generally tend to slow the crack growth. It is shown that the stress intensity factor criterion and the energy-release rate criterion differ when the energetics of the electric field is taken into account. The study of crack tip singular stress field yields a possible explanation for experimentally observed crack skewing in the presence of a strong electric field.