Engineering Plasticity and Its Applications

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Authors: M. Bill Wong
Abstract: The configuration of a steel beam in a concrete/steel composite floor in fire gives rise to a non-uniform temperature profile across the depth of the cross-section. This temperature profile affects the deflection of the steel beam in two ways: thermal bowing due to non-uniform thermal strains and beam deflection due to imposed loads. The beam deflection becomes larger as the elastic properties of the steel beam deteriorate when the temperature is rising. The deflection increases rapidly when the cross-section of the steel beam starts to yield. This paper presents a method for the calculation of the total deflection of a steel beam in a steel/concrete composite floor in fire when the beam is loaded beyond its elastic limit. In this study, the steel beam is assumed to support the concrete floor slab simply at its ends without composite actions.
Authors: Salvatore Federico, Alfio Grillo, Walter Herzog, Gaetano Giaquinta, Shōji Imatani
Abstract: Biological materials can be regarded as composites with spheroidal and fibre-like inclusions, representing cells and collagen fibres, respectively. The orientation and arrangement of the inclusions in a biological tissue is crucial to the determination of the mechanical properties of the material. Furthermore, the reorientation and rearrangement of the inclusions due to the deformation and external forces is of primary interest when dealing with growth and remodelling. We propose to look at the presence of inclusions as a source of internal hyperstaticity: when the material undergoes deformation, a generic inclusion is drifted by the deformation, but at the same time it “feels” the stress field and tends to carry a portion of stress proportional to its stiffness relative to that of the surrounding matrix. With this assumption, we can extend the classical “drift” evolution law for the unit vector field, in order to take the hyperstaticity into account. This method might be used in the description of remodelling in disordered media, such as biological tissues, and may be extended to investigate the reorientation of preferred directions of micro-structural elements in media described with a continuum approach.
Authors: Rie Higuchi, Yoshinori Kanno
Abstract: The main purpose of this study was to investigate the strength and performance of CFRP by using simple fiber-reinforced methods. It shows that the Reef knot has the highest strength in all by an uni-axial loading test. It is confirmed that the outer shape of the CFRP is important to fabricate the strongest structure. It is also attributed that the CFRP joining methods with a smooth contour will improve the connection strength between fiber strands and knot.
Authors: Masamichi Kawai, Akihiro Tanaka
Abstract: Effects of the thickness of plies of the same orientation on the notched strength of symmetric cross-ply CFRP laminates are examined. Three kinds of symmetric cross-ply CFRP laminates with the same total number of plies and the different number and sequence of adjacent laminae of the same orientation are used. Notch sensitivity of those laminates is evaluated for different shapes of notches: double-edge notches (DEN) and a center open hole (CH). Validity of an analytical cohesive zone model (CZM) is evaluated by comparing with experimental results on the three kinds of cross-ply laminates with a center hole. It is clearly observed that the tensile fracture strengths of the DEN and CH specimens significantly reduce as the notch size increases. The sensitivity to notches is highest in the case of alternating cross-ply configuration. The results of this study suggest that additional energy dissipation due to damage around notches should appropriately be considered to estimate the effective fracture toughness used in CZM calculations, especially for a class of cross-ply laminates with lower notch sensitivity.
Authors: Masamichi Kawai, Jian Qi Zhang
Abstract: A macromechanics constitutive model to describe the anisotropic creep behavior of unidirectional composites under off-axis loading conditions is developed with a particular emphasis on accurate prediction of temporal creep softening due to stress variation. A viscoplasticity model that takes account of a combined isotropic and kinematic hardening is adopted as a base for this formulation, and the evolution equation of the kinematic hardening variable is elaborated to enhance the accuracy of prediction of the transient creep softening due to stress variation. Validity of the modified kinematic-hardening viscoplasticity model is evaluated by comparing with the experimental results on unidirectional T800H/3631 carbon/epoxy composites. It is demonstrated that the proposed model can adequately describe the off-axis creep behavior of the unidirectional CFRP laminate under constant and variable stress conditions.
Authors: Souta Kimura, Jun Koyanagi, Takayuki Hama, Hiroyuki Kawada
Abstract: An energy-based analysis has been developed to evaluate interfacial adhesion between fiber and matrix in a single fiber composite over the years. However, the value of the energy-based parameter, e.g. an energy release rate, depends on a stress distribution predicted by a model employed. In the case of carbon fiber-reinforced plastics (CFRP), laser Raman spectroscopy (LRS) is significantly effective to validate the stress distribution predicted. The fragmentation tests with a model of carbon fiber-reinforced epoxy composite are performed, and LRS is used to detect a distribution of the fiber axial strain. An elasto-plastic shear-lag analysis methodology is employed, and a stress distribution is predicted under various approximations of s-s curve of the matrix resin and compared with the experimental results. Our recent energy-balance method, including an energy dissipation induced by plastic deformation around an interfacial debonding tip, is used to calculate an energy release rate to initiate an interfacial debonding (interfacial energy). An effect of the difference between the approximations on the value of the interfacial energy is discussed.
Authors: Nobutada Ohno, Dai Okumura
Abstract: The self energy of geometrically necessary dislocations (GNDs) in single crystals is considered to inevitably introduce a higher-order stress as the work conjugate to slip gradient. It is pointed out that this higher-order stress changes stepwise in response to in-plane slip gradient and thus explicitly influences the initial yielding of polycrystals. The self energy of GNDs is then incorporated into the strain gradient plasticity theory of Gurtin (2002). The resulting theory is applied to 2D and 3D model crystal grains of diameter D, leading to a D-1-dependent term with a coefficient determined by grain shape. This size effect term is verified using published experimental data of several polycrystalline metals. It is thus found that the D-1-dependent term is successful for predicting not only the grain size dependence of initial yield stress but also the dislocation cell size dependence of flow stress in the submicron to several micron range of D.
Authors: Wing Bun Lee, Yi Ping Chen, Sandy To
Abstract: A rate-dependent crystal plasticity constitutive model together with Marciniak- Kuczynski(M-K) approach is employed to perform numerical simulations of forming limits diagrams(FLDs). An initial imperfection in terms of a narrow band is adopted to initialize the sheet necking. Homogeneous deformations inside and outside the band are assumed and the enforcement of compatibility and equilibrium conditions is required only on the band interface. Constitutive computations are carried out on two aggregates of FCC crystal grains, with each representing one of the two zones, respectively. Taylor homogenization assumption is employed to establish the link of stress between single crystal and polycrystal, and to derive an average response of the aggregates. The same initial texture is imparted to the two aggregates and their evolutions will be traced in the necking process. Factors affecting the FLDs prediction, such as imperfection intensity, initial texture, strain rate sensitivity and crystal elasticity will be taken into account. The above procedure will be applied to an annealed aluminium alloy sheet metal
Authors: Ryouji Kondou, Tetsuya Ohashi
Abstract: Slip deformation phenomena in compatible type multi crystal models subjected to tensile load are analyzed by a finite element crystal plasticity analysis code, and accumulation of geometrically-necessary and statistically-stored dislocations (GNDs and SSDs) are evaluated in detail. Crystal orientations for the grains are chosen so that mutual constraint of deformation through grain boundary planes does not take place. We call these models as compatible type multi crystals, because “compatibility requirements” at grain boundaries are automatically maintained by slip deformation only on the primary systems and uniform deformation is expected to occur in each grain. Results of the analysis, however, show non-uniform deformation with high density of GNDs accumulated in a form of band. Growth of such kind of structure of GNDs caused localized accumulation of SSDs at grain boundary triple junctions. Mechanism for the band-shaped accumulation of GNDs in the compatible type multi crystals are discussed from the viewpoint of multi body interactions which arise from shape change of crystal grains after slip deformation.

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