Showing papers on "Fracture mechanics published in 2013"

Fracture Mechanics of Ceramics

Abstract: The failure of ceramic materials is caused by the extension of small flaws. Therefore, linear-elastic fracture mechanics can be applied to describe the failure behaviour. The main problem in the application of the simple fracture mechanics relation is the existence of a rising crack growth resistance curve, which is caused by crack bridging forces behind the advancing crack tip or by transformations in front of the crack tip. The increasing crack growth resistance leads to problems in the transformation of results from specimens with macrocracks to components with natural cracks.

Fracture Behaviour of Polymers

Abstract: 1 Introduction.- I-Mechanics and Mechanisms.- 2 Molecular Aspects.- 3 Fracture Mechanics.- 4 Shear Yielding.- 5 Crazing.- 6 Impact and Fatigue.- II-Materials.- 7 Glassy Polymers I-Thermoplastics.- 8 Glassy Polymers II-Thermosets.- 9 Crystalline Polymers.- 10 Rubbers.- 11 Toughened Multiphase Plastics.- Author Index.

A phase-field model for cohesive fracture

Abstract: In this paper, a phase-field model for cohesive fracture is developed. After casting the cohesive zone approach in an energetic framework, which is suitable for incorporation in phase-field approaches, the phase-field approach to brittle fracture is recapitulated. The approximation to the Dirac function is discussed with particular emphasis on the Dirichlet boundary conditions that arise in the phase-field approximation. The accuracy of the discretisation of the phase field, including the sensitivity to the parameter that balances the field and the boundary contributions, is assessed at the hand of a simple example. The relation to gradient-enhanced damage models is highlighted, and some comments on the similarities and the differences between phase-field approaches to fracture and gradient-damage models are made. A phase-field representation for cohesive fracture is elaborated, starting from the aforementioned energetic framework. The strong as well as the weak formats are presented, the latter being the starting point for the ensuing finite element discretisation, which involves three fields: the displacement field, an auxiliary field that represents the jump in the displacement across the crack, and the phase field. Compared to phase-field approaches for brittle fracture, the modelling of the jump of the displacement across the crack is a complication, and the current work provides evidence that an additional constraint has to be provided in the sense that the auxiliary field must be constant in the direction orthogonal to the crack. The sensitivity of the results with respect to the numerical parameter needed to enforce this constraint is investigated, as well as how the results depend on the orders of the discretisation of the three fields. Finally, examples are given that demonstrate grid insensitivity for adhesive and for cohesive failure, the latter example being somewhat limited because only straight crack propagation is considered.

Finite Element Analysis of Composite Materials using Abaqus

Abstract: Mechanics of Orthotropic Materials Lamina Coordinate System Displacements Strain Stress Contracted Notation Equilibrium and Virtual Work Boundary Conditions Continuity Conditions Compatibility Coordinate Transformations Transformation of Constitutive Equations 3D Constitutive Equations Engineering Constants From 3D to Plane Stress Equations Apparent Laminate Properties Introduction to Finite Element Analysis Basic FEM Procedure General Finite Element Procedure Solid Modeling, Analysis, and Visualization Elasticity and Strength of Laminates Kinematic of Shells Finite Element Analysis of Laminates Failure Criteria Predefined Fields Buckling Eigenvalue Buckling Analysis Continuation Methods Free Edge Stresses Poisson's Mismatch Coefficient of Mutual Influence Computational Micromechanics Analytical Homogenization Numerical Homogenization Local-Global Analysis Laminated RVE Viscoelasticity Viscoelastic Models Boltzmann Superposition Correspondence Principle Frequency Domain Spectrum Representation Micromechanics of Viscoelastic Composites Macromechanics of Viscoelastic Composites FEA of Viscoelastic Composites Continuum Damage Mechanics One-Dimensional Damage Mechanics Multidimensional Damage and Effective Spaces Thermodynamics Formulation Kinetic Law in Three-Dimensional Space Damage and Plasticity Discrete Damage Mechanics Overview Approximations Lamina Constitutive Equation Displacement Field Degraded Laminate Stiffness and CTE Degraded Lamina Stiffness Fracture Energy Solution Algorithm Delaminations Cohesive Zone Method Virtual Crack Closure Technique Appendix A: Tensor Algebra Appendix B: Second-Order Diagonal Damage Models Appendix C: Software Used Index Problems appear at the end of each chapter.

Finite strain fracture of plates and shells with configurational forces and edge rotations

Abstract: We propose a simple and efficient algorithm for FEM-based computational fracture of plates and shells (cf. [1]) with both brittle and ductile materials based on edge rotation and load control. Rotation axes are the crack front nodes and each crack front edge in surface discretizations affects the position of only one or two nodes. Modified positions of the entities maximize the mesh quality complying with the predicted crack path (which depends on the specific propagation theory in use). Compared with XFEM or with classical tip remeshing, the proposed solution has algorithmic and generality advantages. The propagation algorithm is simpler than the aforementioned alternatives and the approach is independent of the underlying element used for discretization. For history-dependent materials, there are still some transfer of relevant quantities between elements. However, diffusion of results is more limited than with tip or full remeshing. To illustrate the advantages of our approach, three prototype models are used: tip energy dissipation (LEFM), cohesive-zone approaches and ductile fracture. Both the Sutton crack path criterion and the path estimated by the Eshelby tensor are employed. Traditional fracture benchmarks, including one with plastic hinges, and newly proposed verification tests are solved. These were found to be very good in terms of crack path and load/deflection accuracy.

Modeling of shear ductile fracture considering a changeable cut-off value for stress triaxiality

Abstract: A macroscopic ductile fracture criterion is proposed based on micro-mechanism analysis of nucleation, growth and shear coalescence of voids from experimental observation of fracture surfaces. The proposed ductile fracture model endows a changeable cut-off value for the stress triaxiality to represent effect of micro-structures, the Lode parameter, temperature, and strain rate on ductility of metals. The proposed model is used to construct fracture loci of AA 2024-T351. The constructed fracture loci are compared with experimental data covering wide stress triaxiality ranging between −0.5 and 1.0. The comparison suggests that the proposed model can provide a satisfactory prediction of ductile fracture for metals from compressive upsetting tests to plane strain tension with slanted fracture surfaces. Moreover, it is expected that the proposed model reasonably describes ductile fracture behavior in high velocity perforation simulation since a reasonable cut-off value for the stress triaxiality is coupled with the proposed ductile fracture criterion.

Failure Criteria for Frp Laminates in Plane Stress

Abstract: A new set of six failure criteria for fiber reinforced polymer laminates is described. Derived from Dvorak's fracture mechanics analyses of cracked plies and from Puck's action plane concept, the physically-based criteria, denoted LaRC03, predict matrix and fiber failure accurately without requiring curve-fitting parameters. For matrix failure under transverse compression, the fracture plane is calculated by maximizing the Mohr-Coulomb effective stresses. A criterion for fiber kinking is obtained by calculating the fiber misalignment under load, and applying the matrix failure criterion in the coordinate frame of the misalignment. Fracture mechanics models of matrix cracks are used to develop a criterion for matrix in tension and to calculate the associated in-situ strengths. The LaRC03 criteria are applied to a few examples to predict failure load envelopes and to predict the failure mode for each region of the envelope. The analysis results are compared to the predictions using other available failure criteria and with experimental results. Predictions obtained with LaRC03 correlate well with the experimental results.

Measurements of the fracture energy of lithiated silicon electrodes of Li-ion batteries.

Abstract: We have measured the fracture energy of lithiated silicon thin-film electrodes as a function of lithium concentration. To this end, we have constructed an electrochemical cell capable of testing multiple thin-film electrodes in parallel. The stress in the electrodes is measured during electrochemical cycling by the substrate curvature technique. The electrodes are disconnected one by one after delithiating to various states of charge, that is, to various concentrations of lithium. The electrodes are then examined by optical microscopy to determine when cracks first form. All of the observed cracks appear brittle in nature. By determining the condition for crack initiation, the fracture energy is calculated using an analysis from fracture mechanics. In the same set of experiments, the fracture energy at a second state of charge (at small concentrations of lithium) is measured by determining the maximum value of the stress during delithiation. The fracture energy was determined to be Γ = 8.5 ± 4.3 J/m2 at s...

A 50-year retrospective review of three-dimensional effects at cracks and sharp notches

Abstract: This review is a brief survey of three-dimensional effects at cracks and sharp notches. The overall aim is to review developments over the past 50 years leading up to the current state of the art. The review is restricted to linear elastic, homogeneous, isotropic materials, with any yielding confined to a small region at a crack or notch tip. It is also restricted to static loading and to constant amplitude fatigue loading. An enormous amount of theoretical and experimental information relevant to three-dimensional effects has been published in the past five decades, so the review is, of necessity, highly selective. Theoretical topics covered are linear elastic fracture mechanics, including Volterra distorsioni, stress intensity factors, corner point singularities, crack front line tension, displacement analysis of cracks and notches, and through thickness distributions of stresses and stress intensity factors. Crack path topics covered are fatigue crack path constraints, determination of fatigue crack paths, oscillating crack fronts in thin sheets and the transition to slant crack propagation in thin sheets. Plane strain fracture toughness testing, including standards, is covered. Overall, it can be concluded that the existence of three-dimensional effects at cracks and sharp notches has been known for many years, but understanding has been limited, and for some situations still is. Understanding improved when the existence of corner point singularities and their implications became known. Increasingly powerful computers made it possible to investigate three-dimensional effects numerically in detail. Despite increased understanding, three-dimensional effects are sometimes ignored in situations where they may be important.

Mechanical properties of ZrB2- and HfB2-based ultra-high temperature ceramics fabricated by spark plasma sintering

Abstract: Flexural strengths at room temperature, at 1400 °C in air and at room temperature after 1 h oxidation at 1400 °C were determined for ZrB 2 - and HfB 2 -based ultra-high temperature ceramics (UHTCs). Defects caused by electrical discharge machining (EDM) lowered measured strengths significantly and were used to calculate fracture toughness via a fracture mechanics approach. ZrB 2 with 20 vol.% SiC had room temperature strength of 700 ± 90 MPa, fracture toughness of 6.4 ± 0.6 MPa, Vickers hardness at 9.8 N load of 21.1 ± 0.6 GPa, 1400 °C strength of 400 ± 30 MPa and room temperature strength after 1 h oxidation at 1400 °C of 678 ± 15 MPa with an oxide layer thickness of 45 ± 5 μm. HfB 2 with 20 vol.% SiC showed room temperature strength of 620 ± 50 MPa, fracture toughness of 5.0 ± 0.4 MPa, Vickers hardness at 9.8 N load of 27.0 ± 0.6 GPa, 1400 °C strength of 590 ± 150 MPa and room temperature strength after 1 h oxidation at 1400 °C of 660 ± 25 MPa with an oxide layer thickness of 12 ± 1 μm. 2 wt.% La 2 O 3 addition to UHTCs slightly reduced mechanical performance while increasing tolerance to property degradation after oxidation and effectively aided internal stress relaxation during spark plasma sintering (SPS) cooling, as quantified by X-ray diffraction (XRD). Slow crack growth was suggested as the failure mechanism at high temperatures as a consequence of sharp cracks formation during oxidation.

Failure mode of spot welds: interfacial versus pullout

Abstract: Spot welds produced via resistance welding have been widely used in the joining of sheet metal for autobodies since the 1950s. Every modern car contains over 2000 spot welds. Failure of the spot weld is therefore an important concern in relation to autobody durability and safety design. Spot welds can fail in two completely distinct modes, namely, nugget pullout failure and interfacial failure. In the present paper, it is first shown that the nugget pullout failure is caused by plastic collapse and the interfacial failure is governed by crack or fracture mechanics. These two failure mechanisms compete with each other and failure of a spot weld occurs when the fracture criterion for one of the mechanisms is satisfied first. Test data from available literature are used to validate the theoretical predictions. Recommendations are made for minimum weld nugget size for a given sheet metal thickness so that nugget pullout failure, the acceptable mode of failure in industry, is ensured.

Hydro‐mechanical modeling of cohesive crack propagation in multiphase porous media using the extended finite element method

Abstract: SUMMARY In this paper, a numerical model is developed for the fully coupled hydro-mechanical analysis of deformable, progressively fracturing porous media interacting with the flow of two immiscible, compressible wetting and non-wetting pore fluids, in which the coupling between various processes is taken into account. The governing equations involving the coupled solid skeleton deformation and two-phase fluid flow in partially saturated porous media including cohesive cracks are derived within the framework of the generalized Biot theory. The fluid flow within the crack is simulated using the Darcy law in which the permeability variation with porosity because of the cracking of the solid skeleton is accounted. The cohesive crack model is integrated into the numerical modeling by means of which the nonlinear fracture processes occurring along the fracture process zone are simulated. The solid phase displacement, the wetting phase pressure and the capillary pressure are taken as the primary variables of the three-phase formulation. The other variables are incorporated into the model via the experimentally determined functions, which specify the relationship between the hydraulic properties of the fracturing porous medium, that is saturation, permeability and capillary pressure. The spatial discretization is implemented by employing the extended finite element method, and the time domain discretization is performed using the generalized Newmark scheme to derive the final system of fully coupled nonlinear equations of the hydro-mechanical problem. It is illustrated that by allowing for the interaction between various processes, that is the solid skeleton deformation, the wetting and the non-wetting pore fluid flow and the cohesive crack propagation, the effect of the presence of the geomechanical discontinuity can be completely captured. Copyright © 2012 John Wiley & Sons, Ltd.

Crumb rubber aggregate coatings/pre-treatments and their effects on interfacial bonding, air entrapment and fracture toughness in self-compacting rubberised concrete (SCRC)

Abstract: The interfacial-bonding, interfacial transition zone (ITZ), and porosity are regarded as the key factors affecting hardened concrete properties. The aim of this study was to experimentally improve the bonding between the rubber aggregate and cement paste by different methodologies including water washing, Na(OH) pre-treatment, and both cement paste and mortar pre-coating. All methods were assessed by determining mechanical and dynamic properties, then correlating this with ITZ porosity and interfacial gap void geometry, along with quantification of the fracture energy during micro crack propagation using fractal analysis. The results indicated that pre-coating the rubber by mortar gave the best results in terms of fracture toughness and energy absorption showing good agreement between observations made at both micro and macro scales.

Bond-Slip Model for FRP Laminates Externally Bonded to Concrete at Elevated Temperature

Abstract: This paper presents a nonlinear local bond-slip model for fiber reinforced polymer (FRP) laminates externally bonded to concrete at elevated temperature for future use in the theoretical modeling of fire resistance of FRP-strengthened concrete structures. The model is an extension of an existing two-parameter bond-slip model for FRP-to-concrete interfaces at ambient temperature. The two key parameters employed in the proposed bond-slip model, the interfacial fracture energy, Gf, and the interfacial brittleness index, B, were determined using existing shear test data of FRP-to-concrete bonded joints at elevated temperature. In the interpretation of test data, the influences of temperature-induced thermal stress and temperature-induced bond degradation are properly accounted for. As may be expected, the interfacial fracture energy, Gf, is found to be almost constant initially and then starts to decrease when the temperature approaches the glass transition temperature of the bonding adhesive; the int...

Post Yield Fracture Mechanics

Abstract: Abstract A simple crack model, which includes a representation of plastic relaxation, is used to discuss the fracture of high and low strength materials in the post yield regime. A correspondence is set up between the fracture criteria given by the present model and the familiar results of linear elastic fracture mechanics. The model is used to discuss the fracture of reinforced composite materials, polymers and turbine and pressure vessel steels. An apparent fracture toughness is defined and it is shown that this quanitity reduces to the plain strain fracture toughness for cases where there is limited plastic deformation. It is found that the plane strain fracture toughness controls the mechanics of fracture even in the post yield regime. The effect of notch root radius on measured fracture toughness values is also discussed.

Salient factors controlling desiccation cracking of clay in laboratory experiments

Abstract: This paper elucidates some of the controlling factors governing soil desiccation. The desiccation tests were conducted on three materials – clay, potato starch and milled quartz sand – all three featuring similar fracture energy. Two controlling factors were identified in desiccation cracking, regardless of the material. The first is the tensile stress and strain energy development within the material when the material is restrained against shrinkage. The distribution of the tensile stress will depend on the boundary conditions and material stiffness, and will dictate where cracks are likely to originate. The second factor is that the exact positions of crack initiations will be controlled by the flaws and/or pores within the material. For materials such as clay, with very fine particles, the cracking mechanism is governed by flaws, since the desaturation of fine pores would require very high suction stress, and this requirement leads to sequential cracking and orthogonal crack patterns. If the material h...