Pressure-dependent Material Research Articles

Design of Dies of Minimum Length Using the Ideal Flow Theory for Pressure-Dependent Materials

This paper develops the ideal plastic flow theory for the stationary planar flow of pressure-dependent materials. Two rigid plastic material models are considered. One of these models is the double-shearing model, and the other is the double slip and rotation model. Both are based on the Mohr–Coulomb yield criterion. It is shown that the general ideal plastic flow theory is only possible for the double slip and rotation model if the intrinsic spin vanishes. The theory applies to calculating the shape of optimal extrusion and drawing dies of minimum length. The latter condition requires a singular characteristic field. The solution is facilitated using the extended R–S method, commonly employed in the classical plasticity of pressure-independent materials. In particular, Riemann’s method is used in a region where all characteristics are curved. It is advantageous since determining the optimal shape does not require the characteristic field inside the region. The solution is semi-analytical. A numerical procedure is only required to evaluate ordinary integrals. It is shown that the optimal shape depends on the angle of internal friction involved in the yield criterion.

Effects of dynamic prestress on silicon carbide ceramic against long rod impact

It is well known that silicon carbide (SiC) ceramic is a pressure dependent material, where the compressive strength increases as the pressure increases. So, it is an effective way to improve the ballistic performance of SiC ceramic by introducing prestress on ceramics surface. In this paper, the concept of dynamic prestress on SiC ceramic by energetic materials was proposed. Five key factors, including the time of projectiles contact targets, velocity of the long rod projectiles (V p), prestress rising stage time (T r), prestress descent stage time (T d) and peak pressure of prestress (P k), were selected to investigate the effect of dynamic prestress on SiC ceramic targets against long rod impact. The effect of dynamic prestress on the ballistic performance of SiC ceramic were investigated, and the dynamic prestress path which can increase the protection capability of SiC ceramic was given. The results indicated that, in most cases, the ballistic performance of the dynamic prestressed SiC ceramic targets against long rod projectiles impact was improved. However, it was also revealed that not all dynamic prestressing can improve the ballistic performance of SiC ceramic targets. It will be benefit to the ballistic performance of SiC ceramic by controlling the prestress time to make sure the moment of the long rod projectile impacts the target in between T 2 and T 4. The sequence of influence degree of each factor on the erosion length of long rod projectile is the velocity of long rod projectiles (V p), prestress descent stage time (T d), peak pressure of prestress (P k) and prestress rising stage time (T r). The erosion length of long rod projectile decreases with the increase of V p, and increases with the increase of prestress descent stage time (T d), peak pressure of prestress (P k) and prestress rising stage time (T r).

Determination of Rate-Dependent Properties in Cohesive Frictional Materials by Instrumented Indentation

The extraction of the elastoplastic constitutive behavior from instrumented sharp indentation is still a subject of research. Several approaches have been proposed to solve this problem, mainly based on the use of numerical techniques. This work proposes an inverse analysis approach based on dimensional analysis calibrated with finite element modeling, to extract the elastoplastic properties from instrumented sharp indentation in rate- and pressure-dependent materials, which is the typical behavior that most polymers exhibit. Pressure sensitivity was modeled with a Drucker-Prager yield criterion, while rate dependency was introduced through a power-law dependence on strain rate of the yield stress. A set of master curves is proposed that relate the experimental metrics of instrumented indentation tests with the parameters of the proposed material model. Furthermore, the analysis was experimentally validated by testing several materials, including PMMA, coarse grain copper, and ultrafine grain copper. The predictions of the inverse analysis correlated well with the known material properties.

Plastic Flow Under Shear-Compression at the Micron Scale-Application on Amorphous Silica at High Strain Rate

A new measurement technique based on microshear has been developed. This technique, inspired from a macroscopic test called the Shear Compression Specimen, was developed at the micron scale by making the specimen using FIB technology, and by compressing it using an in situ SEM nano-indenter. The experimental tests applied on the fused silica show a good repeatability of the data, at low and high strain rates (2000 s−1). Numerical simulation revealed that the deformation in the Microshear Compression Specimen is mainly shear. This approach allows a better understanding of surface shear properties at the micron scale, which is of primary importance for tribological surfaces. It can also help to better understand the surface mechanical properties of pressure dependent materials. Finally, since the shear is applied on a very small gauge in the specimen, it opens the way to very high strain rate experiments (104 s−1 strain rate).

A numerical solver for coupled dynamic simulation of glacial ice impacts considering hydrodynamic-ice-structure interaction

Glacial ice features pose great threats on the safety of ships and offshore structures in the arctic. House sized bergy bits or growlers are of particular concern because of the detection capability limits of marine radars. Analysis and design of structures against collisions from such glacial ice bodies has always been challenging due to the complicated hydrodynamic-ice-structure interaction.This paper proposes a numerical solver for coupled simulation of glacial ice impacts accounting for the effects of hydrodynamic-ice-structure interaction. The solver adopts user subroutines provided in LS-DYNA and combines three different modules, i.e. the BWH (Bressan-Williams-Hill) criterion for the prediction of fracture of steels, a hydrostatic pressure dependent plasticity-based material model for constitutive modelling of ice, and the linear potential flow theory for hydrodynamic loads.The proposed solver is verified and calibrated to ice resistance data from field tests and is then applied to simulate ice collisions on a semi-submersible platform column. Collision scenarios with both in-plane 3DOF and full 6DOF ice motions are considered. The results are discussed with respect to ice motion trajectories, ice crushing and structural damage under the combined action of ice indentation and sliding loads. The dissipated energy predicted by external dynamic models is compared with simulation results and discussed.

Enhancement of Drucker-Prager yield model by adding corner points for pressure-dependent materials

To flexibly describe the pressure-dependent behaviors of materials, Drucker-Prager yield model is enhanced by introducing corner points. We call it piecewise Drucker-Prager (pDP) yield model. Constitutive model is derived by considering strain hardening with non-associative yield flows. Integration algorithm includes the return mapping to corner point. Consistent tangent operator is also formulated, and user material subroutine is written. It is demonstrated that the pDP model is effective in describing the pressure-dependent yield behavior of polymers.

A unified J-Integral-based procedure to investigate at different loading regimes the fracture by FEM simulations and image analysis

This paper presents a robust methodology aimed at assessing the fracture toughness of materials undergoing quasi-static or dynamic loads leading to crack propagation. The proposed implementation relies on the J-Integral concept and it identically operates with data fields obtained by Finite Element modeling or fields experimentally obtained by Digital Image Correlation technique. The capability of the methodology to extract information is put into practice by simulating a FEM-based Single-Edge Notched test specimen undergoing different loading scenarios, from a simple quasi-static linear load increase up to a very aggressive loading pulse that leads to crack propagation and total failure. To do that, the simulated specimen is modeled by an isotropic damageable and pressure-dependent material model that represents a sample made of epoxy resin. The configuration parameters of the J-integral calculation algorithms and the simulation tests are subjected to an extensive parameter study to evaluate the reliability of the calculated static and dynamic energy release rate, with and without crack propagation. From this analysis, a detailed correlation between the instantaneous evolution of the fracture energy and the stress field at every material point is presented and discussed. The proposed method makes it possible to readily track the sequence of propagation and arrest of dynamic cracks.

Effect of specimen geometry on triaxial compressive response of high-strength concrete

The triaxial compressive response of high-strength concrete is needed to understand pressure-dependent material behavior, which is important for modeling extreme loading events. However, nondestructive damage analysis and dynamic triaxial experiments require specimens that are smaller than those typically used for model calibration. Reducing the specimen diameter from 50 mm to 25 mm showed negligible differences in the material response of a high-strength concrete (no coarse aggregate). However, a scalar correction factor is proposed to account for reductions in length-to-diameter ratio (L/D). By isolating size effects, results from experiments with scaled specimens can be implemented for model calibration efforts.

Effect of plastic volumetric strains on shakedown of hardening granular soils

The granular soils are pressure dependent materials and substantial volume change occurs during loading. Some granular soils contract (volume decrease) when sheared and some dilate (volume increase), depending on their initial state. Owing to the plastic volume change that accompanied plastic deformation, the lack of normality rule arises and the granular soil exhibits a non-associated flow rule. As known the non normality has destabilizing effect on the soil behavior in the hardening regime (loss of positive definiteness of the second order work). The unstable behavior usually develops in association with dilation. A contracting soil displaying hardening and stable material behavior under drained conditions, may succumb to unstable flow type when its behavior becomes dilating. This paper deals with the extension of the static shakedown theorem to dilative granular soils in drained conditions, exhibiting pre-failure instability in the hardening regime, in the framework of non associated plasticity.

Plastic-Energy Dissipation in Pressure-Dependent Materials

A thermodynamics-based energy analysis approach for pressure-dependent materials is presented. Formulation of plastic free energy and plastic dissipation for the nonassociated Drucker-Prager plasticity model is derived based on thermodynamics. It is proven that the proposed energy computation formulation always gives nonnegative incremental plastic dissipation, as required by the second law of thermodynamics. The presented methodology is illustrated using numerical simulations of Toyoura sand and Sacramento River sand under different loading conditions. Multidirectional loading and pressure dependency effects on plastic dissipation are investigated. The continuous, nonnegative dissipation of mechanical energy in pressure-dependent frictional materials under complex three-dimensional cyclic loading was properly modeled.

Development of an in-line evaporation unit for the production of gas mixtures containing hydrogen peroxide – numerical modeling and experimental results

Hydrogen peroxide (H2O2) is a typical surface sterilization agent for packaging materials used in the pharmaceutical, food and beverage industries. We use the finite-elements method to analyze the conceptual design of an in-line thermal evaporation unit to produce a heated gas mixture of air and evaporated H2O2 solution. For the numerical model, the required phase-transition variables of pure H2O2 solution and of the aerosol mixture are acquired from vapor-liquid equilibrium (VLE) diagrams derived from vapor-pressure formulations. This work combines homogeneous single-phase turbulent flow with heat-transfer physics to describe the operation of the evaporation unit. We introduce the apparent heat-capacity concept to approximate the non-isothermal phase-transition process of the H2O2-containing aerosol. Empirical and analytical functions are defined to represent the temperature- and pressure-dependent material properties of the aqueous H2O2 solution, the aerosol and the gas mixture. To validate the numerical model, the simulation results are compared to experimental data on the heating power required to produce the gas mixture. This shows good agreement with the deviations below 10%. Experimental observations on the formation of deposits due to the evaporation of stabilized H2O2 solution fits the prediction made from simulation results.

Modeling of granular column collapses with μ(I) rheology using smoothed particle hydrodynamic method

In this paper, to simulate free surface flows of granular materials in a dense regime as a continuum media, a 2D SPH model is developed. The dense flow is characterized as a pressure dependent visco-plastic material based on a local constitutive law to calculate effective viscosity related to local pressure and the norm of strain rate tensor in the numerical method. A simple regularization technique is proposed to reproduce stopping condition and the free surface of a granular flow where the pressure vanishes. Pressure fluctuation as the main drawback of the weakly compressible SPH method leads to an inaccurate pressure distribution. This numerical instability increases at the free surface due to errors associated with the truncated kernels. In this work, a new algorithm is proposed to remove the nonphysical fluctuations by relating divergence of velocity to the Laplacian of pressure. The algorithm is validated for reproducing the dynamics and deposits of collapsing granular columns. The excellent agreement with experimental data is obtained. The maximum thickness of a granular flow on a rough inclined plane is obtained based on the local rheology model. The run-out distances and slopes of the deposits in the simulations also show good agreement with the values found in the experiments.

A new yield criterion for soils with embedded tension cut-off

The object of this paper is the formulation of a new isotropic yield criterion for pressure dependent materials. The main features of the proposed formulation are: (1) variation of the deviatoric profile of the surface with the stress ratio, (2) presence of an embedded tensile cut-off, and (3) high flexibility in shape. Due to the number of parameters of the function, a simple automatic calibration is proposed in order to obtain the set of parameters related to the minimum difference between given experimental or theoretical yield surfaces and the proposed one. Such a simple procedure makes use of an input set of data to be interpreted and of few ghost parameters having a clear meaning. Among the several formulations in literature based on the coupling between a meridian function and a deviatoric function, the proposed criterion is the only one guaranteeing that all possible stress paths are inside the compressive stress domain.

Effect of aging on mechanical properties of high temperature Pb-rich solder joints

The effect of aging on the evolution of interfacial microstructure and mechanical properties of Pb-rich PbSnAg solder joints with different Sn content was investigated. Tensile samples were prepared by soldering two pieces of Ni or Cu strips resulting in joints with gap sizes of about 250 μm. Multi-layered structures composed of Ni coated Si-chips soldered onto Ni/Cu metallized ceramic substrates were used for fatigue testing. All samples were subjected to thermal aging at 250 °C up to 500 h. Microstructural investigations revealed that independent from the substrate material, increased Sn content of the solder alloy results in improvement of the tensile and fatigue properties of the joints and a higher growth rate of the interfacial intermetallic compound (IMC) layers. It was found that the thickness of the wettable substrate especially in the case of low-Sn alloys, also affects the interfacial properties of high temperature PbSnAg solder joints. In this case, a reduced Sn content in solder joints results in weakening of the interface during the reflow process and subsequent thermal aging. The dominant failure mode of the solder joints subjected to cyclic loading was delamination of the interfacial IMC layer from the substrate. Finite element simulations were conducted by using a strain rate and pressure dependent material model for PbSnAg solder in order to analyse the states of stress and strain during static and cyclic loading.

Ideal Flow Theory of Pressure-Dependent Materials for Design of Metal Forming Processes

The ideal flow theory for pressure-dependent materials is used to calculate an ideal die for plane strain extrusion/drawing. In particular, the double slip and rotation and double shearing model are adopted. Comparison with the available ideal flow solution for pressure – independent material is made. It is shown that the die for pressure-dependent material is shorter than that for pressure-independent material. Moreover, the angle of internal friction has an effect of the distribution of contact pressure.

Ideal flow theory for the double – shearing model as a basis for metal forming design

In the case of Tresca’ solids (i.e. solids obeying the Tresca yield criterion and its associated flow rule) ideal flows have been defined elsewhere as solenoidal smooth deformations in which an eigenvector field associated everywhere with the greatest principal stress (and strain rate) is fixed in the material. Under such conditions all material elements undergo paths of minimum plastic work, a condition which is often advantageous for metal forming processes. Therefore, the ideal flow theory is used as the basis of a procedure for the preliminary design of such processes. The present paper extends the theory of stationary planar ideal flow to pressure dependent materials obeying the double shearing model and the double slip and rotation model. It is shown that the original problem of plasticity reduces to a purely geometric problem. The corresponding system of equations is hyperbolic. The characteristic relations are integrated in elementary functions. In regions where one family of characteristics is straight, mapping between the principal lines and Cartesian coordinates is determined by linear ordinary differential equations. An illustrative example is provided.

On Poiseuille flows of a Bingham plastic with pressure-dependent rheological parameters

The plane Poiseuille flow of a Bingham plastic with pressure-dependent material parameters is analysed. Both the plastic viscosity and the yield stress are assumed to vary linearly with pressure and analytical solutions are derived for the two-dimensional pressure and the one-dimensional velocity. The effects of the plastic-viscosity and yield-stress growth parameters on the thickness of the unyielded plug and the conditions for the occurrence of flow are discussed.

Stress and strain fields in rotating elastic/plastic annular disks of pressure-dependent material

ABSTRACTThe Drucker–Prager yield criterion is used in conjunction with its associated flow rule to find the elastic/plastic stress and strain distributions within the rotating annular disks under plane stress conditions. The main distinguished feature of the model, as compared to typical models used for analysis of disks, is that the material is plastically compressible. Using an approach proposed elsewhere, the solution for strain rates is reduced to one nonlinear ordinary differential equation and two linear ordinary differential equations. These equations can be solved one by one, which significantly simplifies the numerical treatment and increases the accuracy of solution.

Numerical assessment of gray cast iron notched specimens by using a triaxiality-dependent Cohesive Zone Model

A triaxiality-dependent Cohesive Zone Model for the numerical prediction of failure loads of notched specimens under different loading modes is presented. Since the cohesive crack is modeled by means of the embedded crack approach, one can express the cohesive parameters with variables from the continuum, such as pressure or triaxiality. The model is validated by its application to two experimental campaigns previously developed by the authors on notched specimens subjected to mode I and III loadings respectively, made of gray cast iron, a strongly pressure dependent material.

Low-order mixed finite element analysis of progressive failure in pressure-dependent materials within the framework of the Cosserat continuum

PurposeThis paper aims to develop a finite element analysis strategy, which is suitable for the analysis of progressive failure that occurs in pressure-dependent materials in practical engineering problems.Design/methodology/approachThe numerical difficulties stemming from the strain-softening behaviour of the frictional material, which is represented by a non-associated Drucker–Prager material model, is tackled using the Cosserat continuum theory, while the mixed finite element formulation based on Hu–Washizu variational principle is adopted to allow the utilization of low-order finite elements.FindingsThe effectiveness and robustness of the low-order finite element are verified, and the simulation for a real-world landslide which occurred at the upstream side of Carsington embankment in Derbyshire reconfirms the advantages of the developed elastoplastic Cosserat continuum scheme in capturing the entire progressive failure process when the strain-softening and the non-associated plastic law are involved.Originality/valueThe permit of using low-order finite elements is of great importance to enhance computational efficiency for analysing large-scale engineering problems. The case study reconfirms the advantages of the developed elastoplastic Cosserat continuum scheme in capturing the entire progressive failure process when the strain-softening and the non-associated plastic law are involved.