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Silicon carbide foam is a promising material for high-temperature use because it has excellent thermal shock resistance and strength, low thermal conductivity, and excellent chemical resistance. Up till now SiC foam was analyzed under quasi-static compression and 4- and 3-point bending. This paper attempts for the first time to numerically analyze the SiC foam properties under impact conditions. Using the peridynamical approach it was possible to describe damage initiation, its dynamical growth, and the final fragmentation of the foam. The major conclusions resulting from the analysis are that for high impact velocities damage initiates much earlier compared to low-velocity impact, and the modes of failure are qualitatively different.

The subject of the study is the deformation of the oxygen-free high conductivity copper. The copper sample is given in the form of a foam. The sample undergoes an impact into an elastic wall. The strain rate hardening effect is investigated. The numerical model of the open-cell foam skeleton is prepared in the framework of the peridynamics method. The dynamic process of compression with different impact velocities is simulated. It has been found that the strain rate hardening effect is essential for the load-carrying capacity of the material under study. Taylor impact test of solid cylinder analysis precedes the analysis of the metallic foam.

Ceramic composites are used in such industries as the armaments industry, aviation, automotive, nuclear power, and space exploration. In several areas, they stand for the source of technological progress. The material is often subjected to extreme loads, such as variable dynamic loads and high temperatures. Peridynamics is a non-local, meshless quite recently formulated method of stress analysis. The methods appear to be useful in the analysis of brittle materials. In the paper, an impact model of an Al2O3/ZrO2 a thin plate is investigated. A brittle damage model is used for both phases of the composite. The attention is focused on damage initiation and distribution in the impacting sample.

WC/Co composite is a standard hard material used for the production of cutting tools. It has both very good thermo-mechanical and wear properties. During the cutting, process tools are subjected to impact loading and gradual degradation due to high-stress concentrations. This loading induced deterioration is complex process still not well investigated and explained. Up till now the dynamic response of the WC/Co composite was analysed under dynamic impulse compressive loading [1]. However, the behaviour of the above two-phase composite under impacts conditions was not investigated in details. In the presented micromechanical approach the real material structure geometry of the internal structure can be performed including spatial distribution of: (1) WC grains and their dimensions, (2) volume content of plastic Co binder with their thickness, (3) system of grain/binder interfaces and (4) cracks initiated and developed during impulse loading, (5) possible brittle grains rotation. The results reveal the dependence of the microcracking processes and the stress distribution on impact velocity and presence of discontinuities in the Co binder and the interface zone between the binders and the grains. The microcracks system was evaluated by the damage parameter according to Kachanov, 1986 [62].

Degradation of Cermet Materials (CM) under impact and pulse pressure is not thoroughly investigated. In this study, we qualitatively compare the behaviour of WC/Co samples under these types of loading. The new models of impact and dynamic compressive load of a WC/Co plate were investigated. We developed two models of the composite plate, namely, a continuous model and a model with crack appearance possibility in the interfaces/binders. We noted a qualitative difference of the shapes of the deformed structure due to different models and kind of loading. The differences also concern the Mises stress, equivalent plastic strains and damage parameter. The proposed models are suitable for both impact and pressure load. The possibility of cracks appearance should not be neglected. In case of the model with discontinuities, for both kinds of loads, the grains rotation and sliding is more distinct than in case of the continuous model.

Cutting tools are manufactured among others from cermet (e.g. WC/Co) having excellent mechanical properties. Geometry of the internal microstructure is complex and mechanical response due to quasi-static or dynamic loading is difficult to be described. Particularly, the dynamic loading is not investigated enough precise up till now. Experimental evidences, e.g. Siegl and Fischmester (1988), Ravichandran (1994), indicate that the fracture energy of WC/Co is expended through ductile failure of the Co: (1) near the binder/tungsten carbide interface or by (2) dimple rupture across the interphase. Concentrations of stresses around grain boundaries lead to initiation of microcrack system, which is dispersed for dynamic loading. The aim of the paper is to extend the previously formulated models (Sadowski et al., 2005, 2006, 2007, Debski and Sadowski, 2014, 2017) of the polycrystalline composite towards more advanced finite element formulation, applicable for description of the cermet behavior under dynamic pulses. The model takes into account: (1) spatial distribution of the cermet constituents, (2) system of grain boundaries/binder interfaces modeled by interface elements, (3) rotation of brittle grains. The obtained results show that stress distributions and gradual microcracking processes are quite different for quasi-static and dynamic loadings. It was revealed by damage parameter indicating concentration of microcracks.

Cermet Materials (CM), for example, WC/Co, have very good mechanical, thermal and wear properties. They are used for manufacturing of cutting tools. However, their behavior under dynamic loads is still not properly understood. Experiments, e.g. Siegl and Fischmester (1988) and Ravichandran (1994), indicate that the fracture energy of WC/Co is expended through ductile failure of the Co: (1) close to the binder/tungsten carbide interface (Liu et al., 2017) [64] or by (2) dimple rupture across the interphase (Sigl and Exner, 1987) [22] . Stress concentrations around grain boundaries lead to initiation of microcracks which are dispersed by dynamic loading. The main goal of the paper is to investigate the previously formulated models of the two-phase composite (Sadowski et al., 2005, 2006, 2007; Debski and Sadowski, 2014, 2017) [47] , [48] , [49] , [50] , [51] in the case of dynamic compressive pulses that are common in the case of cutting tools. We have taken into account complex spatial distribution of cermet phases, grain/binder interfaces modeled by interface elements, possibility of cracks appearance within binders using interface elements as well, and rotation of brittle grains. The obtained results show that microcracking process and stress distributions are different for quasi-static and dynamic loadings. Early development of microcracks distribution revealed by damage parameter was observed.

Ceramic composites (CCs) are mixtures of different phases, and their development is often regarded as a milestone in technological progress. They are used in practically all significant industries. Frequently, CCs are exposed to variable dynamic loads, impacts or high temperatures [1-3]. In this paper, the impact of thin plates fabricated from Al2O3/ZrO2 is analyzed. The plates are made of the above CC with different proportions of its components. Damage progression is analyzed using peridynamics, similarly to quasi-static tension [4]. The purpose of the study is to describe the impact damage development in the CC plates and determine the role of phase contents. It has been found that phase ratios in the tested CC are vital for the behavior of the plates. In conclusion, it can be claimed that the employed peridynamic approach is suitable for solving the problems under study and that the impacting plates should be treated as real three-dimensional structures.

Metal-ceramic composite (MCC) materials can be used for manufacturing high-responsibility structures such as jet engines or cutting tools. One example of these materials is a two-phase wolfram carbide (WC) and cobalt (Co) composite. This MCC is a combination of hard WC grains with a Co metallic ductile binder. The resulting microstructure is a combination of two phases with significantly different mechanical behaviors. In this study, we investigate impact conditions, starting with an illustrative example of the Taylor impact bar where&mdash, although the process is very rapid&mdash, the equivalent plastic strain and temperature are higher in the adiabatic solution than those in the coupled solution. On exposing the WC/Co composite with a metallic binder to impact loading, heat is generated by plastic deformation. If the process is fast enough, the problem can be treated as adiabatic. However, a more common situation is that the process is slower, and the heat is generated in the ductile metallic binders. As a result, the associated grains are heated due to the conduction effect. Consequently, the process should be treated as coupled. When the impact is applied over a short time period, maximum temperatures are significantly lower if the process is analyzed as coupled rather than as adiabatic. The grains are immediately affected by temperature increase in the binders. Therefore, the heat conduction effect should not be omitted.

This paper presents some advances of finite element explicit formulation for simulation of metal forming processes. Because of their computational efficiency, finite element programs based on the explicit dynamic formulation proved to be a very attractive tool for the simulation of metal forming processes. The use of explicit programs in the sheet forming simulation is quite common, the possibilities of these codes in bulk forming simulation in our opinion are still not exploited sufficiently. In our paper, we will consider aspects of bulk forming simulation. We will present new formulations and algorithms developed for bulk metal forming within the explicit formulation. An extension of a finite element code for the thermomechanical coupled analysis is discussed. A new thermomechanical constitutive model developed by the authors and implemented in the program is presented. A new formulation based on the so-called split algorithm allows us to use linear triangular and tetrahedral elements in the analysis of large plastic deformations characteristic to forming processes. Linear triangles and tetrahedra have many advantages over quadrilateral and hexahedral elements. Linear triangles and tetrahedra based on the standard formulations exhibit volumetric locking and are not suitable for large plastic strain simulation. The new formulation allows to overcome this difficulty. New formulations and algorithms have been implemented in the finite element code Stampack developed at the International Centre for Numerical Methods in Engineering in Barcelona. Numerical examples illustrate some of the possibilities of the finite element code developed and validate new algorithms.

WC/Co metal-matrix ceramic composites (MMCs) are used for manufacturing cutting and drilling tools, surgical tools, mill inserts, jet engines, and other high-responsibility structures. The combination of a phase of hard wolfram carbide (WC) grains with a metallic ductile interface of cobalt (Co) yields a complex microstructure with significantly different mechanical properties of the phases. The aim of this study is to investigate the thermomechanical behavior of the MMC polycrystalline material with ductile binders under impact conditions. An adiabatic and coupled thermomechanical analysis of the WC/Co composite under impact loading is performed using FEM. The heat conduction is considered in the analysis in order to capture heat transfer in the polycrystalline structure, i.e. between the grains and the grain boundaries (GBs). The Johnson-Cook yield function is used in the constitutive model of the ductile Co interface, while the WC phase is linear elastic. The motivation comes from the observation that the heat conductivity effect is often omitted, even in recent papers **[75]. Significant differences between temperatures and plastic strains in the adiabatic and coupled solutions are observed, which leads to the main conclusion that the adiabatic solution should not be used for assessing the impact response of the composite material.

The aim of the paper is to develop the previously formulated model [19, 20] of the polycrystalline composite to include porosity growth at metallic interfaces of metal–ceramic composites (MCCs). Examples of this kind of MCCs are: (1) a two-phase material composed of brittle grains WC joined by the plastic binder Co, which can contain a small degree of porosity introduced during the cooling process [31], (2) TiC–Mo2C hard phase grains surrounded by tough binder phase Ni [12]. This work focuses on the description of the deformation of the MCC material including the modelling of a real material internal structure taking into account porosity growth during the loading. Experimental observations of the WC/Co composite [10] indicate that the majority of the fracture energy of MCC is expended through ductile failure of the plastic binder Co (dimple rupture across the binder or in the binder near the binder/carbide interface). This process is preceded by porosity growth at metallic interfaces and finally leads to...

PurposeThis paper sets out to present developments of a numerical model of squeeze casting process.Design/methodology/approachThe entire process is modelled using the finite element method. The mould filling, associated thermal and thermomechanical equations are discretized using the Galerkin method. The front in the filling analysis is followed using volume of fluid method and the advection equation is discretized using the Taylor Galerkin method. The coupling between mould filling and the thermal problem is achieved by solving the thermal equation explicitly at the end of each time step of the Navier Stokes and advection equations, which allows one to consider the actual position of the front of the filling material. The thermomechanical problem is defined as elasto‐visco‐plastic described in a Lagrangian frame and is solved in the staggered mode. A parallel version of the thermomechanical program is presented. A microstructural solidification model is applied.FindingsDuring mould filling a quasi‐static Arbitrary Lagrangian Eulerian (ALE) is applied and the resulting temperatures distribution is used as the initial condition for the cooling phase. During mould filling the applied pressure can be used as a control for steering the distribution of the solidified fractions.Practical implicationsThe presented model can be used in engineering practice. The industrial examples are shown.Originality/valueThe quasi‐static ALE approach was found to be applicable to model the industrial SQC processes. It was found that the staggered scheme of the solution of the thermomechanical problem could parallelize using a multifrontal parallel solver.

The present contribution focuses on the problem of the mechanical response of a polycrystalline ceramic material containing intergranular layers. The internal structure of the material was modelled using eight-noded isotropic hexagonal finite elements to represent grains and interfaces. Two kinds of the material were analysed numerically. Both were made up of elastic grains, but in the first case the interface layers were elastic and had different properties in comparison to the grains. In the second case, the interphase had visco-plastic properties. The paper considers the influence of the initial heterogeneity of the material on the stress and displacement distribution inside the polycrystalline material subjected to uniaxial tension. One can observe local stress concentrations at the so-called “triple points” and on the surface of the material. These can act as cracks initiators. Additionally, the influence of the viscosity parameter of the interface material was investigated.

This paper deals with the evaluation of the effects of initial stresses developed during the pressurized casting process. The stresses are induced by the external pressure applied to the cast and developed due to thermal loading. The effect of the stresses is considered as a second order effect by means of investigating the influence of the ‘geometric’ or ‘initial stresses’ stiffness matrix on the response of the cast. The problem formulation is done in the updated Lagrangian (UL) frame. An implicit time integration scheme is applied to solve the transient thermomechanical problem in a staggered form. The constitutive mechanical model is elasto-viscoplastic with hardening incorporated with a Mises yield function. The finite element method is employed and a few 3D numerical examples are presented.

Finite element formulations for structural sensitivity analysis of non-linear systems with fixed overall shape are discussed. Both the direct differentiation and adjoint variable methods are employed. The resulting sensitivity algorithms are consistent with time integration scheme adopted for solving equilibrium problem. Effectiveness and computational aspects of the procedures are discussed and compared. Numerical algorithms are shown to be readily implemented in existing finite element codes. Large-scale examples illustrate the paper.

The aim of this presentation is to show the behaviour of a cellular composite material. The material is two-phase consisting of metallic, relatively rigid interfaces and weak filling material. Such type of a generic composite is used as core filler between external layers of sandwich composite material applied in aerospace engineering. We investigate the limit load of a sample varying the initial void ratio in the filling. We are using the Tvergaard-Gurson in order to describe porosity existence in the material and elasto-plastic models with the assumption of presence of the finite deformations. The geometrical model is three-dimensional.

The aim of this paper is to present a constitutive model in the case of an uniaxial tension of the polycrystalline materials including the inter-granular metallic layers, creating its internal structure. The paper is focused on the discussion of the elastic properties of a composite components influence on the overall material response. The effective continuum model was applied to get the constitutive relations. Representative Volume Element (RVE) was analysed taking into consideration an initial internal structure of the material obtained from SME photographs. Owing to a high complexity of the internal structure of the composite material, FEA technique was used to get macroscopic stress-strain correlations. They include gradual changes of the internal structure of the material due to porosity and cracks development under tension.

A novel constitutive numerical model for predicting the time-dependent mechanical response of a polycrystalline ceramic material containing finite thickness inter-granular layers is proposed. The material consists of elastic grains, whereas the inter-granular layers have visco-plastic properties. The material structure was modelled using eight-noded isotropic hexagonal finite elements both for the grains and the interfaces. The paper presents results from an investigation into the influence of the initial heterogeneity of the material on the stress and displacement distribution inside the polycrystalline material when subjected to uniaxial tension. In some parts of the polycrystalline structure, local stress concentrations can be observed both on the surface and inside the material. These can initiate defects in the form of pores, cracks, etc. In this paper, the influence of the viscosity parameter of the interface material on the overall material response is also described.

PurposeTo present a numerical model of squeeze casting process.Design/methodology/approachThe modelling consists of two parts, namely, the mould filling and the subsequent thermal stress analysis during and after solidification. Mould filling is described by the Navier‐Stokes equations discretized using the Galerkin finite element method. The free surface is followed using a front tracking procedure. A thermal stress analysis is carried out, assuming that a coupling exists between the thermal problem and the mechanical one. The mechanical problem is described as an elasto‐visco‐plastic formulation in an updated Lagrangian frame. A microstructural solidification model is also incorporated for the mould filling and thermal stress analysis. The thermal problem is solved using enthalpy method.FindingsDuring the mould‐filling process a quasi‐static arbitrary Lagrangian‐Eulerian (ALE) approach and a microstructural solidification model were found to be applicable. For the case of the thermal stress analysis the influence of gap closure, effect of initial stresses (geometric nonlinearity), large voids and good performance of a microstructural model have been demonstrated.Research limitations/implicationsThe model can also be applied to the simulation of indirect castings. The final goal of the model is the ability to simulate the forming of the material after mould filling and during the solidification of the material. This is possible to achieve by applying arbitrary contact surfaces due to the sliding movement of the cast versus the punch and die.Practical implicationsThe presented model can be used in engineering practice, as it incorporates selected second‐order effects which may influence the performance of the cast.Originality/valueDuring the mould‐filling procedure a quasi‐static ALE approach has been applied to SQC processes and found to be generally applicable. A microstructural solidification model was applied which has been used for the thermal stress analysis only. During the thermal stress analysis the influence of gap closure and initial stresses (geometric nonlinearity) has been demonstrated.

The paper deals with an overview of some industrial applications leading to a formulation for advanced numerical techniques. The applications comprise squeeze casting processes, forming of tablets and petroleum reservoir modelling. All of the problems lead to solutions of highly nonlinear, coupled sets of multiphysics equations.

A computational finite element model is developed to predict the load-deflection characteristic of portal frames with semi-rigid welded and bolted joints. Plate components of frame members and joints are modelled by thin shell finite elements while bolt connectors by springs with the force-deformation characteristic evaluated from test results. The computer software ABAQUS is used. Experimental investigations were designed in order to evaluate frame load-deflection characteristics, joint local rotations, failure modes, and the contribution of end-plates and bolt connectors to the joint rotations. Theoretical results of frame load-deflection characteristics predicted with use of ABAQUS program are compared with the experimental results. The modelling of friction effect between the contact surfaces of bolted joints is verified to be the most important factor. The comparative analysis leads to the conclusion that the proposed advanced shell model can be very useful in the verification of simplified models being developed for practical applications. (Botswana Journal of Technology: 2003 12(2): 51-61)

Publisher Summary This chapter discusses the finite element model (FEM) as part of the wider research program carried out at the Warsaw University of Technology on the quasi-cyclic and quasi-static behavior of steel semi-rigid joints and frame specimens. Theoretical and experimental investigations were concerned with portal frame specimens composed of I section members and welded or bolted joints. A computational FEM is developed to predict the load-deflection characteristic of portal frames with semi-rigid welded and bolted joints. Frame member and joint plate components are modeled by thin shell finite elements, while bolt connectors, by springs with the force-deformation characteristic evaluated from test results. The computer software ABAQUS is used. Experimental investigations were designed to evaluate frame load-deflection characteristics, joint local rotations, and the contribution of end plates and bolt connectors to the joint rotations. Theoretical results of frame load-deflection characteristics predicted with the use of ABAQUS program are compared with the experimental results. The modeling of friction effect among the contact surfaces of bolted joints is verified. The comparative analysis leads to the conclusion that the proposed advanced shell model can be very useful in the verification of simplified models being developed for practical applications.

This chapter deals with the formulation and implementation of frictional boundary conditions. The presented method excludes the necessity of usage of interface elements. The key point of the presented contact algorithm is the choice of a local coordinate system that allows it to establish uniquely, the states of slip and stick. This is done by applying at the contact point a conical coordinate system in which the total contact force vector lies on the meridian of the cone. The algorithm is formulated in incremental form and the slipstick conditions are checked in implicit manner. The Coulomb friction law is taken into account. The presented method is the direct extension of the developments concerning 2D problem presented in. The algorithm is implemented into an Eulerian finite element program simulating the 3D flow of a bulk material. In addition, the presented description is also applicable to simulation of other problems—for example, metal forming processes, where the friction prevails. Numerical examples illustrating the correctness of the presented method are provided.

This chapter deals with the simulation of three-dimensional silo flow of a bulk material. Most of the numerical simulations of the flow in silos are usually done in two dimensions what cannot fully reflect all effects observed in real silos. The goal of this chapter is to provide an effective numerical tool to analyze this type of silos including different types of silos including various inserts. The description of the problem is Eulerian and Drucker-Prager type yield function is used. The solution consists of the following three steps: elastic initial stage, creep state and the flow. All of the stages are nonlinear because friction between the flowing material and the walls is considered. The constitutive equations governing the material behavior are solved implicitly and the algorithmic tangent moduli are used. The 4 and 10 nodes tetrahedral elements are used. A finite element program based on the aforementioned assumptions is being developed. This program is the 3D extension of a program described in. Numerical examples of complex geometry silo showing the current capabilities of the program developed are presented.

Publisher Summary This chapter presents a project to develop a 3D computational finite element method model of double butt prestressed bolted connections taking into account the effects of bolts, initial gaps, friction, and prestressing force. This model may be used especially for investigation of the connections deformability, also after first slip not taken into account in the method of structures analysis used in the everyday engineering practice. There are some design parameters that are considered: initial yield stress, hardening modulus, friction coefficient, and prestressing force magnitude. To deal with these effects, a finite element model is created. The computational model is developed in the framework of ABAQUS general-purpose program. The connection is discretized with about 7500 3D-isoparametric brick elements. All parts of the connection are separated. Initial gaps are assumed among all of the elastic bodies and later, during the loading process, non-elastic bodies, and the contact surfaces are established. The proposed model is verified by experiments. The 20 specimens that are the connections in technical scale are investigated. Comprising the results obtained theoretically, as well as in experiment, shows that the 20 specimens differ insignificantly; it means that the proposed model can take advantage in workout of simplified models used in everyday engineering practice.

This paper presents the application of an explicit dynamic finite element code for simulation of metal forming processes, of both sheet and bulk forming. The experiences reported here have been gained during the development and use of our own explicit program Stampack. An original formulation of a triangular shell element without rotational degrees of freedom is reviewed combining the explicit sheet forming simulation with the implicit springback analysis as well as the parallelization of the explicit program described. An extension of a finite element code for coupled thermomechanical analysis is discussed. A new thermomechanical constitutive model developed by the authors and implemented in the program is presented. Numerical examples illustrate some of the possibilities of the finite element code developed.

An incremental finite element formulation for structural sensitivity analysis or nonlinear (possibly path dependent) systems with fixed overall shape is proposed. Both the direct differentiation and adjoint variable methods, as well as a mixed differentiation-adjoint technique are employed to evaluate 1st- and 2nd-order sensitivity increments during the load step. Numerical illustration is given.