Properties Of Hardened Material Research Articles

Strain ratcheting of steel tubulars with a rectangular defect under axial cycling: A numerical modeling

Cyclic axial loads in tubular steel sections might lead to local buckling, wrinkling and accumulation of plastic strains in the tube. For example, this can be caused by repetitive start-up/shutdown and temperature changes in an offshore pipeline which generates cycles of axial compression/relaxing in the line. During their life time steel tubes may also experience material loss due to corrosion or wall thinning. The current paper reports the result of a numerical modeling of ratcheting behavior of steel tubes with a rectangular defect under cyclic axial loadings. The tubes have been initially subjected to monotonic axial compression beyond initiation of small amplitude wrinkles and subsequently to persistent axial cyclic loads. A nonlinear isotropic/kinematic (combined) hardening model has been adopted for the material, which its parameters have been obtained from cyclic tests conducted on small coupon specimens. The results of the numerical simulation have been compared with experimental data. In general, a reasonable agreement has been noticed between the experimental and the numerical results for the ratcheting behavior of the tubes. It is shown that surface imperfections have a very pronounced effect on the ratcheting response of the defected tubes, as compared to the monotonic responses. The model has also been used to study effects of some key factors such as the initial strain level, the stress amplitude, the mean stress, the loading regime, wall thinning and the material hardening properties on the ratcheting response and on the progressive plastic buckling of steel tubes with a rectangular defect.

Development of Experimental Method to Improve Sheet Metal Formability by Transverse Normal Stress

To make full use of the promotion potential of hydrostatic stress on the formability of sheet metal, several foundational questions met in practical application of double-sided pressure forming technique are studied in this paper. The theoretical analysis of sheet metal deformation during the double-sided pressure bulging process is carried out, and an analytical approximation for normal pressure loading path that secures out-of-plane stress ratio, γ, continuously increasing (dγ ≥ 0 holds) is presented. Utilization of the relationship between the theoretical approximation for normal pressure load and material hardening properties, a novel double-sided pressure forming method is proposed—the viscous pressure bulging (VPB) of the overlapping sheet metals, in which a highly viscous but flowable semi-solid medium is used as the soft die and the target sheet metal is deformed under the constraints from viscous medium on one side and overlapping sheet on another side. To confirm the efficiency of the proposed method, the VPB test of overlapping sheet metals is simulated by DEFORM-2D, and the experimental tests are also carried out. The results show that σ3 provided by overlapping sheet can overcome the diminishing of γ value caused by evolving strain-hardening and geometric softening effect in the post-diffuse necking stage. The experimental obtained increase of the limit dome height (LDH) of double-sided pressure bulging specimen is 12.6% compared with that of single-sided pressure bulging specimens.

Semi-analytic inversion method for the determination of elastoplastic properties of power hardening materials from limited torsional experiment

An inverse problem related to the determination of elastoplastic properties of a beam is considered within J2 deformation theory. A new fast algorithm is proposed for the identification of elastoplastic properties of engineering materials. This algorithm is based on finding the three main parameters of the unknown curve g(ξ2) (plasticity function), namely, the elasticity limit , the modulus of rigidity G and the strain hardening exponent κ. The advantage of this algorithm is that only two values of measured output data are required for the reconstruction of the unknown function g(ξ2). Note that all parameterization algorithms use numerous torsional experiments as necessary data for the determination of only some part of the unknown stress–strain curve. Numerical examples related to applicability and high accuracy of the proposed approach are presented for the cases of noise free and noise data.

An analysis of Gurson model with parameters dependent on triaxiality based on unitary cells

Abstract The Gurson model is widely used in the continuum-mechanics framework to analyse the ductile fracture process promoted by the nucleation, growth, and coalescence of voids. Further works improved the original Gurson model by introducing two parameters, q 1 and q 2 , to adjust model predictions to the numerical results of a periodic array of cylindrical and spherical voids in hardening materials. This modified model is known as the Gurson–Tvergaard (GT) model. Commonly, these parameters are considered constants or dependent only on the material-hardening properties. However, there is evidence that these parameters also depend on the triaxiality of the stress field, as well as on initial porosity. In this work, a consistent fully implicit integration of the constitutive equations of the GT model, considering the q-parameters dependent on the triaxiality and the initial porosity of the stress field, is presented, and the corresponding consistent tangent operator is proposed. The model is validated by comparing the stress–strain behaviour, as well as the evolution of void volume fraction, of a voided cell and the equivalent cell of GT material with dependent parameters. The cases considered correspond to variable triaxiality stress fields, present in non-proportional loading conditions.

Investigation of rotating hollow cylinders of strain-hardening viscoplastic materials by sequential limit analysis

The paper employs sequential limit analysis to investigate rotating hollow cylinders of nonlinear isotropic strain-hardening viscoplastic materials. A computational optimization procedure was developed to account for hardening material properties and weakening behavior corresponding to the strain-rate sensitivity and widening deformation. A sequence of limit analysis problems was then conducted to seek the corresponding plastic limit angular velocities sequentially by a general algorithm incorporated with an inner and outer iterative sequence. Particularly, analytical solutions of plastic limit angular velocities and the onset of instability were derived for rigorous comparisons. The corresponding stability condition was also obtained explicitly. Specifically, the implicit form of the onset of instability was solved by the fixed point iteration. It is found that the computed limit angular velocities are rigorous upper bounds and match well with analytical solutions.

On the uniqueness and sensitivity issues in determining the elastic and plastic properties of power-law hardening materials through sharp and spherical indentation

A systematic study of the uniqueness, reversibility and sensitivity issues associated with seven indentation-based methods of property extraction demonstrates that: (i) The indentation algorithms generally identify the elastic and plastic properties of materials uniquely for most materials. (ii) The indentation forward algorithms (wherein the indention responses are determined from the elastic and plastic properties of the indented materials) and the reverse algorithms (wherein the elastic and the plastic properties of materials are extracted from the indentation responses) are distinct for each indentation method and are internally consistent in that the differences in the elastic and plastic properties determined through the reverse analysis and the ‘true’ material properties are generally small for a large number of materials, for each of the seven methods. (iii) While the differences in the indentation response parameters predicted by each of the seven indentation methods (for a particular material) could be small, there could be considerable dispersion in the elastic and plastic properties predicted by the reverse algorithms of the seven methods (for a particular set of indentation response parameters). (iv) In the forward analysis, small uncertainties in the elasto-plastic properties lead to small uncertainties in the predictions of the indentation response of materials. The sensitivity distribution is generally heterogeneous and symmetric across positive and negative variations in the material elasto-plastic properties. (v) In the reverse analysis, the elastic modulus exhibits low sensitivity, while the yield strength and the strain-hardening exponent generally exhibit high sensitivity to uncertainties in the indentation response parameters. The sensitivity distribution is heterogeneous and asymmetric across positive and negative variations in the indentation response parameters. (vi) The representative stresses are fairly robust to uncertainties in the indentation response parameters. Consequently, dual sharp and spherical indentation methods, which identify multiple representative stresses, exhibit reduced sensitivity in the determination of the plastic properties.

Analytical and numerical investigation of strain-hardening viscoplastic thick-walled cylinders under internal pressure by using sequential limit analysis

Plastic limit load of strain-hardening viscoplastic thick-walled cylinders subjected to internal pressure is investigated numerically and analytically in the paper. The paper applies sequential limit analysis to deal with the quasi-static problem involving hardening material properties and weakening behavior corresponding to the strain-rate sensitivity and widening deformation. By sequential limit analysis, the paper treats the plasticity problems as a sequence of limit analysis problems stated in the upper bound formulation. Rigorous upper bounds are acquired iteratively through a computational optimization procedure with the internal pressure factor as the objective function. Especially, rigorous validation was conducted by numerical and analytical studies of thick-walled cylinders in terms of the plastic limit load as well as the onset of instability. It is found that the computed limit loads are rigorous upper bounds and agree very well with the analytical solutions.

Final report of RILEM TC 188-CSC ‘Casting of self compacting concrete’

Increased productivity and improved working environment have had high priority in the development of concrete construction over the last decade. Development of a material not needing vibration for compaction—i.e. self-compacting concrete (SCC)—has successfully met the challenge and is now increasingly being used in routine practice. The key to the improvement of fresh concrete performance has been nanoscale tailoring of molecules for surface active admixtures, as well as improved understanding of particle packing and of the role of mineral surfaces in cementitious matrixes. Fundamental studies of rheological behaviour of cementitious particle suspensions were soon expanded to extensive innovation programmes incorporating applied research, site experiments, instrumented full scale applications, supporting technology, standards and guides, information efforts as well as training programmes. The major impact of the introduction of SCC is connected to the production process. The choice and handling of constituents are modified as well as mix design, batching, mixing and transporting. The productivity is drastically improved through elimination of vibration compaction and process reorganisation. The working environment is significantly enhanced through avoidance of vibration induced damages, reduced noise and improved safety. Additionally, the technology is improving performance in terms of hardened material properties like surface quality, strength and durability.

AVALIAÇÃO EXPERIMENTAL DOS PARÂMETROS DE TENACIDADE CTOD E INTEGRAL J EM ESPÉCIMES DE FLEXÃO SE(B) UTILIZANDO O MÉTODO ETA

This work presents an estimation procedure to determine the fracture toughness parameters J and CTOD for SE(B) specimens using the eta method. The main purpose is to obtain numerically calibrated η (eta) factors which are applicable to an extensive range of relative crack dimensions (0.05 ≤ a/W ≤ 0.7) and material hardening properties. The analysis results enable the construction of functional forms which describe the variation of the η factors with crack size (a/W) and material hardening properties, n. The procedure provides more accurate toughness values of J and CTOD from laboratory experimental measurements of fracture toughness.

HARDENED MATERIAL PROPERTIES OF SELF‐COMPACTING CONCRETE

Self‐compacting concrete (SCC) is an innovative construction material with a favourable rheological behaviour, which is caused by its modified concrete composition. Based on this fact SCC offers improved fresh concrete but also hardened material properties and therefore many advantages regarding the productivity and the design potential compared with normal vibrated concrete. Consequently, the amount of SCC, used for structural purposes has strongly increased worldwide in the last years. In this context it is necessary to know, if it is possible to apply the current design rules, eg Model Code 90 and Eurocode 2, that are based on years of experience on normal vibrated concrete, to structural members made of SCC as well. This paper represents the analysis of own and internationally published test results of the compressive strength, tensile strength, modulus of elasticity, bond behaviour and the time‐dependent deformations of SCC in comparison with conventional concrete, in order to give a general statement regarding the agreements and differences between the hardened material properties of these concretes.

Hardened material properties of self‐compacting concrete

Self‐compacting concrete (SCC) is an innovative construction material with a favourable rheological behaviour, which is caused by its modified concrete composition. Based on this fact SCC offers improved fresh concrete but also hardened material properties and therefore many advantages regarding the productivity and the design potential compared with normal vibrated concrete. Consequently, the amount of SCC, used for structural purposes has strongly increased worldwide in the last years. In this context it is necessary to know, if it is possible to apply the current design rules, eg Model Code 90 and Eurocode 2, that are based on years of experience on normal vibrated concrete, to structural members made of SCC as well. This paper represents the analysis of own and internationally published test results of the compressive strength, tensile strength, modulus of elasticity, bond behaviour and the time‐dependent deformations of SCC in comparison with conventional concrete, in order to give a general statement regarding the agreements and differences between the hardened material properties of these concretes. First Published Online: 14 Oct 2010

Dynamic buckling of elastic–plastic square tubes under axial impact—I: stress wave propagation phenomenon

The speeds of the stress waves that can propagate in an elastic–plastic medium with isotropic linear strain hardening in a plane stress state are obtained in order to analyse the influence of the transient deformation process on the initiation of buckling in square tubes under axial impact. The kinematic conditions across a surface of discontinuity were employed to obtain the stress wave propagation speeds for an initial condition [ v x ]= V 0. It is shown that the plastic wave speeds depend on the stress state and on the direction of wave propagation. The material hardening properties have a stronger effect on the speed of the slow plastic wave, while the shear stress affects both the speeds of the fast and slow plastic waves. The magnitude of the instantaneously applied in-plane load [ σ xx ] at t=0, which results from an impact in the direction (n x=1, n y=0) , is obtained as a function of the initial velocity V 0 when using the differential relationships along the characteristics. A numerical simulation of an in-plane impact on a finite plate by a large mass with an initial velocity shows that the predicted stress wave speeds from the theoretical analysis agree with the speed of the propagation of the plastic zone in the plate. It is shown that the initial buckling pattern forms within a sustained axial plastic flow and remains unchanged when large displacements develop. Therefore, it is concluded that the transient process in elastic–plastic plates subjected to an in-plane impact plays a significant role for the formation of the final buckling shape and this process can be analysed using estimates for the stress wave speeds obtained for an elastic–plastic medium in a plane stress state.

Deforming Mesh for Computational Aeroelasticity Using a Nonlinear Elastic Boundary Element Method

A nonlinear elastic boundary element method (NBEM) approach is developed as an innovative deforming mesh generator for computational aeroelastic simulation. The computational fluid dynamics (CFD) mesh is assumed to be embedded in an infinite nonlinear elastic medium of a hardening material, leading to the formulation of a pseudononlinear elastostatic problem. Whereas the CFD surface mesh is treated as a boundary element model and the CFD flowfield grid as domain sample points, the NBEM approach solves Navier's equations using a particular solution scheme that removes the requirement of the domain integral in the conventional NBEM formulation. The NBEM approach has a unified feature that is applicable to all mesh systems, including unstructured, multiblock structured, and overset grids. An optimization strategy is employed to determine the optimum hardening material properties by minimizing the mesh distortion in the viscous region where grid orthogonality must be preserved. Three test cases are performed to demonstrate the robustness and effectiveness of the NBEM approach for deforming mesh generation.

Dynamic buckling of an imperfect elastic, visco-plastic plate

Finite element analyses of dynamic buckling of an initially pre-bent plate are compared with static and dynamic experiments on type II columns investigated by Tam and Calladine (Int J Impact Engng 1991;11: 349–77). We employ an elastic–visco-plastic material model of the Cowper–Symonds type, which includes the measured quasi-static effective-stress plastic–strain curve. The striker is represented by a point mass impacting a contact surface on the end of a plate. The analysis considers models composed of two-dimensional beam- and three-dimensional shell-elements and discusses the effects caused by the finite width of the plate, the strain- and strain-rate hardening material properties and inertia. The calculated static and dynamic response is in good agreement with the experimental curves. Having shown the accuracy of our finite element model, the effect of the impact velocity on the structural response is analysed.

Technical note The influence of air entrainment on the properties of silica fume concrete

An experimental study on fresh and hardened properties of silica fume concrete containing air-entraining agent was performed. Silica fume content ranged from 0 to 20% by mass of the cementitious materials (cement plus silica fume). Air content in fresh mix concrete ranged between 2 and IS%. Fresh mix properties were characterized by determining the slump and air content. Hardened material properties such as compressive and flexural strength and permeability were investigated. Test results showed that air entrainment reduces the mechanical properties of silica fume concrete. It was also shown that air entrainment has a minimal effect on the permeability of concrete with high silica fume content.

Properties of Polypropylene Fiber Reinforced Concrete

An experimental research investigation of the fresh and hardened material properties of the fibrillated polypropylene fiber reinforced concrete is reported. Fiber lengths were 1/2 and 1/4 inch, and volume fractions were 0.1, 0.3, and 0.5%. Fiber effects on concrete properties were assessed. Properties studied were slump, inverted slump cone time, air content, compressive and flexural behaviors, impact resistance and rapid chloride permeability, and volume percent of permeable voids. An innovative method of characterizing the flexural behavior of fibrillated polypropylene fiber concrete was proposed. The new method was dependent on the post-peak flexural resistance of concrete. For impact resistance and flexural behavior, it was concluded that 1/4-inch-long fibers were more effective than 1/2-inch-long fibers for volumes of 0.3% or less, while 1/2-inch-long fibers were more effective for 0.5% volume.

Uniqueness and stability of rigid-plastic cylinders under internal pressure and axial tension

Uniqueness of deformation and stability of the equilibrium configuration of a long closed-ended cylinder of rigid-plastic material, obeying the von Mises yield criterion, are examined under internal pressure and axial tensile load. Sufficient conditions are derived for uniqueness of the current state of the finitely deformed cylinder. By considering a material model of the Ramberg-Osgood type, it is shown that uniqueness is guaranteed up to a stage when either of the loads (or both) attains a maximum. For such a material model, “pressure-tension interaction curves” are obtained for some values of the wall-ratio and the strain-hardening index. Under internal pressure and small tension, however, the possibility of a bifurcation preceding a stability loss is shown to exist for certain cylinder geometry and material hardening properties.

Bifurcation and instability modes in thick-walled rigid-plastic cylinders under pressure

Rigid-plastic strain-hardening flow in closed-end cylinders under internal and external pressure is examined from the view-point of obtaining criteria for uniqueness and stability of finite deformation. A general velocity field, satisfying constitutive requirements at a generic instant, is constructed and employed to investigate the possibility of loss of steady-state deformation. Earlier stability bounds, for the case of internal pressure, derived under the assumption that instability occurs in a continuation of the steady-state mode, may then be verified, although with some restrictions as it is shown that, for certain combinations of cylinder geometry and material hardening properties, non-unique deformation might precede a stability loss. For the case of external pressure, a general criterion is established from which the accuracy of the classical tangent-modulus buckling load may be confirmed in the thin-shell approximation.