Papers by Keyword: Mixed-Mode

Abstract: Multi-parameter fracture mechanics concept has been applied to investigate crack behavior under mixed-mode loading, particularly in a semi-circular bending disc. The so-called Williams’ series expansion is used for the crack-tip stress field approximation. It has been shown that application of the generalized fracture mechanics concept can be crucial for materials with specific fracture behavior, such as elastic-plastic or quasi-brittle one, when fracture occurs not only in the very vicinity of the crack tip, but also in a more distant surrounding. Then, considering the higher-order terms of the Williams’ expansion in fracture criteria can be helpful. The attention is devoted to the analysis of the influence of various distances between the supports during the three-point bending test on the results of the further crack propagation direction.

Abstract: The suitability of an optimisation workflow for the determination of the mixed-mode cohesive zone model parameters using digital volume correlation (DVC) data and the inverse finite element method was examined. A virtual compression experiment of a cylinder with a spherical inclusion was modelled using the finite element method. A bilinear traction separation law with a linear mixed-mode relationship was used to describe the interfacial behaviour. Known mode I and mode II fracture energies, = 20 J/m² and = 40 J/m² and damage initiation stress, = 0.09 MPa, were used to generate a target composite debonding behaviour. An objective function,, determined based on the debonding behaviour measurable by DVC was chosen. A full factorial experiment was carried out for the four cohesive parameters and showed that correlation between fracture energies/ damage initiation stresses and is non-linear and discontinuous with multiple local minima. Optimisations initiated at the local minima identified from the full factorial experiment correctly determined the target cohesive fracture energies and damage initiation stresses.

Abstract: Many efforts have been made recently to determine the fracture toughness of different types of foams in static and dynamic loading conditions. Taking into account that there is no standard method for the experimental determination of the fracture toughness of plastic foams, different procedures and specimens were used. This paper presents the polyurethane foam fracture toughness results obtained experimentally for three foam densities. Asymmetric four-point bending specimens were used for determining fracture toughness in mode I and in a mixed one, and also the influence of the loading speed and geometry of the specimen were investigated.

Abstract: A mathematical model for analysis of contact delamination problems has been developed and implemented into the program Matlab by means of the Symmetric Galerkin Boundary Element Method (SGBEM). The SGBEM numerical algorithm enables to exploit an energetic formulation which governs interface rupture. A rate-independent model of the delamination process is obtained, considering an interface damage variable. A numerical algorithm has been proposed to provide maximallydissipative local solution which yields numerically stable time-discretization. The developed 2-dimensional sample example of mathematical model demonstrates the model behaviour and its suitability in many aspects of engineering practise.

Abstract: This paper presents a new method to conveniently calculate the stress intensity factors for the cracked flattened Brazilian disks under mixed-mode loading. The finite-element method is employed to confirm an assumption that the formula of the stress intensity factors for the cracked Brazilian disk subjected to pressure can be directly used to calculate the stress intensity factors for the cracked flattened Brazilian disk. The calculated results show that the assumption is valid and reliable. The calculated results also confirm that the Saint-Venant’s principle is still valid in fracture mechanics. In addition, the present paper proposes a concept of optimum load distribution angle.

Abstract: In order to study the Mixed-Mode cracking behavior of cold recycling mixes with emulsified asphalt, the Arcan test configuration was chosen to perform the fracture characteristics of cold recycling mixes in five levels of Mixed-Mode (100, 75, 50, 25 and 0% Mode I) at three loading rates (1.0mm/min, 0.5mm/min, 0.1mm/min). The load and load-line displacement, peak load, crack angle and fracture energy were all used for further analysis. The process of cracking can be divided into three stages: the stage of crack arises, expand stage, and the brittle break stage; 0% Mode I has a significant difference from the others; the loading rates and levels of Mixed-Mode both have great influence on peak load; the higher level of Mode I usually gets lower crack angle; the fracture energy of 100% Mode I ranges from 168 J/m2 to 308 J/m2 and the specimen in 0.5mm/min has greater fracture energy.

Abstract: For a slant pre-crack under mixed-mode conditions, a method is proposed in which mode Ⅰ and mode Ⅱ stress intensity factors ‹K_I›_mes and ‹K_II›_mes can be directly evaluated from the discontinuous displacement along it. The effect on fatigue pre-crack deformation behavior was discussed by comparing fatigue and annealed cracks. In general, using the biggest tangential stress criterion the direction propagating from the pre-cracks can be predicted by ‹K_I›_mes and ‹K_II›_mes calculated above. So testing for bending fatigue crack propagation under mixed-mode conditions was carried out using fatigue and annealed slant pre-cracks with slant angle β=450 defined as the angle between loading and pre-crack direction in a rectangular plate. As a result, for annealed pre-crack, the estimated fracture angle θ_estcorresponded to the measured oneθ_mes ; On the other hand, for fatigue pre-crack,θ_mes is bigger than θ_est because of the compressive residual stress around the pre-crack .

Abstract: For a slant pre-crack under mixed-mode conditions, a method is proposed in which mode Ⅰ and mode Ⅱ stress intensity factors(K_I)_mes and (K_II)_mes can be directly evaluated from the discontinuous displacement along it. The effect on fatigue pre-crack deformation behavior was discussed by comparing fatigue and annealed cracks. In general, using the biggest tangential stress criterion the direction propagating from the pre-cracks can be predicted by (K_I)_mes and (K_II)_mes calculated above. So testing for bending fatigue crack propagation under mixed-mode conditions was carried out using fatigue and annealed slant pre-cracks with slant angle β=450 defined as the angle between loading and pre-crack direction in a rectangular plate. As a result, for annealed pre-crack, the estimated fracture angle θ_est corresponded to the measured one θ_mes; On the other hand, for fatigue pre-crack,θ_mes is bigger than θ_est because of the compressive residual stress around the pre-crack.

Abstract: The superposition-finite element method is developed to analyze the mixed-mode delamination in laminated composites. Both a coarse global mesh and an overlaying fine local mesh are integrated into the finite element analysis model. The whole design domain is discretized by a uniform global mesh, while the high stress regions are discretized by fine local meshes. Local mesh is built independently from the global mesh, which greatly simplifies the model generation procedures. Strain energy release rate is calculated based on the modified virtual crack closure-integral method, which is used to describe the propagation of delamination in laminated composites. Mixed-mode bending tests are performed for unidirectional and cross-ply carbon fiber reinforced laminated composites to characterize the interlaminar fracture behavior under mixed-mode I/II loading conditions. The interlaminar fracture toughness is also given for different mixed-mode ratio. It is seen that fracture resistance for laminated composites exhibit R-curve behavior (increase as delamination propagation). However, once the delamination is sufficiently long, the interfacial fracture toughness changes slightly as the delamination extended and become almost independent of the delamination length. The results of finite element method are in good agreement with the experimental results and provides a basis for establishing failure criterion used in damage tolerance analysis of composite structures.

Abstract: Objectives: Numerical determinations of Stress Intensity Factors (SIFs) for a shaft under mixed-mode load with a crack of different sizes in the connection zone between square and circular cross-sections. Methods: Linear-elastic Fracture Mechanics principles are used. The numerical analysis program used was ABAQUS CAE version 6.9-3. The shaft consists in a circular section and a square section, with a fillet connecting zone. Cracks of different lengths and different depths are modeled. The shaft is subjected to torsion and bending. The SIFs were determined using the contour integral method. Results: The stress distribution was determined and plotted, and the stress concentration effect of the notches was highlighted. Crack propagation was also performed, using the XFEM module of ABAQUS code. The computed SIFs were plotted along the crack front. Conclusions: Crack initiation and propagation matched the pattern obtained in experimental tests, thus validating the model. The results confirmed that the fillet zone between the two sections acts as a stress concentrator. The fillet radius determines the magnitude of stress concentration. Crack geometry has a significant influence on SIFs, as well as on the global stress distribution.