Delamination of Grain-Interfaces in Silicon Nitride

Intergranular cracking due to delamination of grain interfaces along with the development of bridging grains is the most important mechanism for the high fracture toughness of silicon nitride. In this line, an interface behavior, which is extending the Coulomb friction concept into the tensile domain has been implemented into a thermodynamical consistent frame work of Helmholtz free energy and dissipation. The model is used to describe the fracture process in a simple model geometry with a β-Si₃N₄ grain embedded into a precracked matrix of oxynitride glass. The material model considers the thermoelastic anisotropy of the grain and the thermal residual stresses, which evolve during the cooling of the model from the glass transition temperature to room temperature. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Strength and fracture properties of advanced SiC-based fibers

The tensile strength and the fracture properties of advanced SiC-based fibers were characterized, and an extensive fractographic analysis was conducted to correlate their mechanical behavior and microstructure. Tensile tests re vealed that the strength of Hi-Nicalon™ and Hi-Nicalon™ Type S fibers was sensitive to a critical flaw. The inspection of fracture surfaces revealed that the fracture of these fibers originated mainly at the critical flaw, which was surrounded by an obvious mirror zone. The Tyranno™-SA fiber showed a transcrystalline fracture behavior. The different fracture behavior observed in this work could be related to different fabrication processes and compositions at the grain boundary. For the Hi-Nicalon™ and Hi-Nicalon™ Type S fibers, the critical flaw size was linearly related to the mirror size. By using the linear fracture mechanics, the fracture toughness and the critical fracture energy of the fibers were estimated. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 6, pp. 759–770, November–December, 2006.     

An evaluation of the interlaminar fracture toughness of a thermoplastic composite with offset centre flies

Conclusion The offset DCB specimen has been used to characterize the influence of cooling rate and loading rate on the interlaminar fracture properties of carbon fibre reinforced PEEK. By offsetting the mid-plane fibres by several degrees, the amount of fibre bridging occurring during fracture has been reduced considerably. It has been shown that IM6 carbon fibre PEEK is quite sensitive to the cooling conditions employed after consolidation at 380 °C. Low rates of cooling yield a high level of crystallinity and a reduced fracture toughness. The modified DCB specimen has been successfully applied to highlight a distinct interlaminar fracture rate sensitivity. The high rate properties of this material still leave cause for concern and more work is required before these materials will find widespread use.Published in Mekhanika Kompozitnykh Materialov, No. 4, pp. 476–483, July–August, 1992.     

Prediction of fracture toughness of embrittled steels by means of the Small Punch Test

To characterise the randomly distributed strength and fracture toughness of brittle steels, many specimens have to be destroyed. Since the Small Punch Test (SPT) needs only little material, it is a well suited experiment, when only a small volume of material is available. In this study the cleavage fracture of a ferritic steel at low temperature was investigated using the Beremin model. The failure probability is described with a 2-parameter Weibull distribution in terms of the so-called Weibull stress, which is calculated using an elastic-plastic finite element stress analysis. While the transfer of Weibull parameters works well between similar geometries and loading conditions, it works bad in more general cases. Modifications of the Beremin model are necessary to overcome this problem. Recent publications consider a lower threshold value of the Weibull stress, which leads to a lower Weibull modulus and therefore to a stronger volume size effect of strength. The suitability of this approach to transfer cleavage fracture results from SPT to fracture mechanics specimens was investigated. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modelling of cracks on different scales in ferroelectric materials

In this work we study contributions to the effective fracture toughness of ferroelectric materials arising from effects on macroscopic and mesoscopic scales of the system. On the macroscopic scale, the crack in a ferroelectric material is modeled taking into account an extended theory of stresses at interfaces in dielectric solids [1-3]. We predict several new effects, such as the “poling effect”, “collinear effect” and the coupling of a Mode-II shear loading and the Mode-I SIF. Further, on the mesoscopic scale, we study the influence of polarization switching limited to the fracture process zone (small scale switching) on the fracture toughness. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

一种预测界面裂纹形成的新方法

本文提出了一种预测界面裂纹形成的新方法,称为“β=0法”.这是一种变换方法,通过调整有关材料弹性常数,把振荡应力场变换为非振荡应力场.界面韧性曲线将随调整后新的材料性质而改变.本文方法预测的临界荷载与界面断裂力学预测的临界荷载严格一致.最后通过几个实例说明了保持能量释放率不变的情况下,怎样实施β=0法.     

A fragmentation model with neighborhood interaction

Several models of fragmentation have been studied that suppose random fracture forces. In this article, we did a numerical study on a dynamic model for fragmentation in which the fracture forces are generated by neighboring fragments and are proportional to the size of the common boundary between two fragments. The following assumptions were also considered: the material defects are represented by a random distribution of point flaws; the total mass is conserved; and the iterative fracture of each fragment is randomly stopped by a condition that considers a constant probability and a minimal fragment size. The motivation for this model was to determine under what circumstances a continuous fragmentation model with fracture forces defined by the neighbors’ interaction produces results that are in agreement with the experimental evidence. The main result of this work establishes that the fragment size distribution follows a power-law for fragments of greater area than the minimal fragment size m_fs. The visualizations present complex fracture patterns that resemble real systems.     

Strength vs. toughness optimization of microstructured composites

Aim of this paper is to present a new fractal approach linking the macroscopic mechanical properties of micro- and nano-structured materials with the main parameters: composition, grain size and structural dimension, as well as contiguity and mean free path. Assuming the key role played by the interfaces, the proposed fractal energy approach unifies the influences of all the above parameters, through the introduction of a fractal structural parameter (FSP), which represents an extension of the Gurland’s structural parameter. This modeling approach is assessed through an extensive comparison with experimental data on poly crystalline diamond (PCD) and WC–Co alloys. The results clearly show that the theoretical fractal predictions are in a fairly good agreement with the experiments on both hardness and toughness. This new synthetic parameter is thus proposed to investigate, design and optimize new micro- and nano-grained materials. Eventually, FSP-based optimization maps are developed, that allow to design new materials with high hardness and toughness.     

Computational mechanics-based modeling of size-dependent hardening in polycrystals

It has been well-known for a number of years that the macroscopic material response of polycrystalline metals is influenced by the size and morphology of grains. Different size effects may occur, one of which is the Hall-Petch effect. The key aim of this contribution is the computational modeling of grain-size-dependent hardening in polycrystals using a microstructural approach. Here, the focus is on the influence of the microscopic grain boundary conditions on the simulation results. In particular, micro-flexible boundary conditions are discussed and compared to micro-hard and micro-free assumptions. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Toughening effect of ferroelectric ceramics induced by domain switching and dislocations

The multi-scale analysis of fracture toughness of ferroelectric ceramics under complicate mechanical–electrical coupling effect is carried out in this paper. The generalized stress intensity factor (SIF) arising from spontaneous strains and polarization transformation in switching domain zones is accurately obtained by using an extended Eshelby theory. Taking BaTiO₃ ferroelectric ceramic for example, it is discovered that the crack propagation can be induced by domain switching arising from negative electrical field when the crack surface is parallel to the isotropic plane, and the obtained critical electric displacement intensity factor (EDIF) approximates closely to that obtained by the Green’s function method. Additionally, as pinning dislocations and slip dislocations can strongly influence properties of ferroelectric devices and induce the property degradation, it is necessary to investigate the dislocation toughening effects on fatigue and fracture mechanisms. The results show that the dislocation shielding and anti-shielding effects on mode II SIF, mode I SIF and EDIF are obviously different when a dislocation locates at a position near the crack tip. Through the calculation of the critical applied EDIF for crack propagation by using mechanical energy release rate (MERR) theory, it is discovered that the slip angles obviously influence fracture toughness, and the mode II SIF arising from dislocation has little influence on fracture toughness, however, the mode I SIF and EDIF arising from dislocation have great influences on fracture toughness.     

Equilibrium cracks in composites reinforced with unidirectional fibres

A discrete-continuum approach, proposed by Novozhilov for analysing the equilibrium states of a brittle of crack in an isotropic body, is applied to a penny-shaped crack situated in a fibre-reinforced composite perpendicular to the fibres. The structural non-uniformity of the material is taken into account by the presence of unbroken fibres in the narrow part of the crack, adjoining the edge, and the different effect of the strength properties of the fibre and matrix on the limit state of the crack. Using this model, the range of dimensions of equilibrium cracks is established and an estimate is given of the critical size of the bridged part of the crack, corresponding to the onset of catastrophic fracture. It is shown that this dimension has the same value for a penny-shaped crack and for a crack under plane strain, does not depend on the form of the load and, under the condition of its smallness, is a brittle fracture characteristic of a fibre-reinforced material. The possibility of using this fracture model for two types of ceramics is analysed on the basis of experimental data.     

A coupled phase-field model for ductile fracture in crystal plasticity

The objective of this work is to present a simplified, nonetheless representative first stage of a phenomenological model to predict the crack evolution of ductile fracture in single crystals. The proposed numerical approach is carried out by merging a conventional well- stablished elasto-plastic crystal plasticity model and a well-known phase-field model (PFM) modified to predict ductile fracture. A two-dymensional initial boundary-value problem of ductile fracture is introduced considering a single crystal Nickel-base superalloy material. the model is implemented into the finite element context subjected to a one-dimensional tension test (displacement-controlled). (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Micromechanical modeling of twinning

There exist material models that incorporate mechanical twinning in a homogenized sense, or consider specific aspects, like grain refinement or texture evolution. However, since the RVE-technique became a standard method, it is possible to obtain more detailed predictions based on micromechanical models. In this work, an approach based on a nonconvex elastic potential and the corresponding results of FE calculations are presented. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A strong discontinuity based adaptive refinement approach for the modeling of crack branching

In the current work, the physical phenomena of dynamic fracture of brittle materials involving crack growth, acceleration and consequent branching is simulated. The numerical modeling is based on the approach where the failure in the form of cracks or shear bands is modeled by a jump in the displacement field, the so called ‘strong discontinuity’. The finite element method is employed with this strong discontinuity approach where each finite element is capable of developing a strong discontinuity locally embedded into it. The focus in this work is on branching phenomena which is modeled by an adaptive refinement method by solving a new sub-boundary value problem represented by a finite element at the growing crack tip. The sub-boundary value problem is subjected to a certain kinematic constraint on the boundary in the form of a linear deformation constraint. An accurate resolution of the state of material at the branching crack tip is achieved which results in realistic dynamic fracture simulations. A comparison of resulting numerical simulations is provided with the experiment of dynamic fracture from the literature. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Explicit energy-minimizers of incompressible elastic brittle bars under uniaxial extension

A rectangular bar made of a hyperelastic, but brittle, incompressible homogeneous and isotropic material is subject to uniaxial extension. We prove that the energy minimizers are, depending on the toughness coefficient of the material, either the homogeneous deformation, or the family of deformations for which a horizontal fracture breaks the material in two rectangular pieces, each of which is a rigid motion of the undeformed piece.     

Fracture propagation in a boron-aluminum composite

Conclusions 1. Application of the linear mechanics of fracturing to composites of the boron-aluminum type is justified, since it has proven possible to determine in an experiment the value of the fracture strength which characterizes the resistance of the material to fracture.2. The fracture strength of boron-aluminum turns out to be higher than the same characteristic of the matrix material. Boron-aluminum is a material with a high resistance to fracture, whose surface is normal to the direction of the fibers. The fracture work of boron-aluminum with a fiber content of 50% is approximately three times higher than the fracture work of the unreinforced matrix.3. At present there is no computational model of a composite which would permit reliably estimating the value of the fracture strength and optimizing a composite for this characteristic. Such a model should intrinsically take account of the statistical characteristics of a fiber.4. The data obtained can also be interpreted as confirmation of the existence of a scaling dependence of the strength of a composite in the case of supercritical reinforcement.Institute of Solid-Body Physics, Academy of Sciences of the USSR, Moscow. Translated from Mekhanika Polimerov, No. 6, pp. 1010–1017, November–December, 1976.     

Optimization model of recrystallization hot rolling of titanium-vanadium steels

An optimization model was built based on the data of a pilot-scale (4.5 MN load, 225 KW power capacity) rolling mill to minimize the austenite grain sizes of Ti–V steels, which prevail at the instant of completion of the static recrystallization during hot rolling. A computer program developed for this optimization model was run for the rolling schedule, which is designed according to the complete recrystallization case. An energy optimization model developed previously was applied to different rolling schedules. The grain size optimization results demonstrate the effectiveness of these modelling approaches in terms of final grain size, final plate thickness, measured and computed roll force and torque values for both the design of the thermomechanical schedules which produce plate with fine-grained microstructures, high strength, and notch toughness and the temperature-reduction schedules of conventional controlled rolling.     

Numerical crack path prediction considering orthotropic effects and experimental verification

For a reliable prediction of crack paths, on the one hand the accurate calculation of crack tip loading quantities is inevitable, on the other hand orthotropic features of the fracture toughness need to be taken into account. The interplay of crack tip loading and material response due to fracture is still unclear and seems to have a crucial effect on crack path predictions. Numerical tools for the accurate calculation of crack tip loading quantities using path-invariant J-integrals and interaction integrals (I-integral) are presented. Here, global approaches are beneficial when considering crack tips approaching other crack faces or internal boundaries. Curved crack faces have to be taken into account and special treatment regarding crack face integrals is necessary. Experimental investigations are carried out at standard CT-specimens of rolled aluminum alloy Al-7075 exhibiting a directional orthotropy of the fracture toughness. Considering that property, the numerically predicted crack paths based on FE calculations show very good agreement with subcritically grown paths obtained from experiments. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mode I,mode II,and mixed-mode I/II interlaminar fracture toughness of GFRP influenced by fiber surface treatment

The interlaminar fracture behavior of unidirectional glass fiber reinforced composites with fiber surface treatment has been investigated in modes I and II and for fixed mode I to mode II ratio of 1.33. The data obtained from these tests have been analyzed by using different analytical approaches. The present investigation is focused on the influence of the glass fiber surface treatment on the interlaminar fracture toughness of unidirectional laminates. Glass fibers with two different fiber surface treatments have been investigated. fiber surface treatment was carried out by using a polyethylene or silane coupling agent in combination with modifying agents. The glass fibers were embedded in the brittle epoxy matrix. Mode I, mode II, and mixed-mode I/II tests were performed in order to determine critical strain energy release rates. Double cantilever beam (DCB), end-notched flexure (ENF), and mixed-mode flexure (MMF) specimens were used. For both types of fiber surface treatment about the same values of mode I initiation fracture toughness G_IC ^init were obtained. It was observed that in mode I interlaminar crack growth in the DCB test for the composite sized by polyethylene, the crack propagation is accompanied by extensive fiber bridging. For both fiber surface treatments interlaminar fracture toughness increases considerably with increasing of crack length. For the fiber surface treatment with the silane coupling agent, the value of mode II initiation fracture toughness G_IIC ^init was about 2.5-times higher in comparison with that of a composite sized by polyethylene. For both types of fiber surface treatments the mixed-mode I/II test has shown a similar behavior to the mode I DCB test.     

Interlaminar Crack Propagation Analysis of ENF Specimens Based on the Cohesive Zone Model北大核心CSCD

Based on the classical laminated plate theory and the cohesive zone model, a theoretical model for general delamination cracked laminates was established for crack propagation of pure mode Ⅱ ENF specimens. Compared with the conventional beam theory, the proposed model fully considered the softening process of the cohesive zone and introduced the nonlinear behavior of ENF specimens before failure. The predicted failure load is smaller than that under the beam theory and closer to the experimental data in literatures. Compared with the beam theory with only fracture toughness considered, the proposed model can simultaneously analyze the influences of the interface strength, the fracture toughness and the initial interface stiffness on the load-displacement curves in ENF tests. The results show that, the interface strength mainly affects the mechanical behavior of specimens before failure, but has no influence on crack propagation. The fracture toughness is the main parameter affecting crack propagation, and the initial interface stiffness only affects the linear elastic loading stage. The cohesive zone length increases with the fracture toughness and decreases with the interface strength. The effect of the interface strength on the cohesive zone length is more obvious than that of the fracture toughness. When the adhesive zone tip reaches the half length of the specimen, the adhesive zone length will decrease to a certain extent. Copyright ©2022 Applied Mathematics and Mechanics. All rights reserved.