Effective Strain Rate Research Articles

Deformation characteristic of the precision forging of a blade with a damper platform using 3D FEM analysis

A blade with a damper platform is one of the most important types of blades being developed in aeronautical engines. However, this type of blade is complicated in shape, consisting of four feature parts with different geometrical shapes. Besides obvious flow of material along the transverse direction, there is material flow along the longitudinal body during its forging process. In addition, the material used is difficult to deform. All these have a significant influence on the precision forging process of the blade. Thus, it is necessary to choose some feature sections along the transverse and longitudinal direction of blade and systematically understand the deformation characteristics of blade forging process. In this paper, by means of 3D rigid–viscoplastic FEM simulation of the precision forging process of the blade, the deformed meshes, distributions of some field variables, including velocity, effective strain, effective strain rate and effective stress are presented for the four chosen feature cross-sections and the velocity fields are obtained for a selected typical longitudinal feature section, and further the deformation characteristics of forging this blade have been revealed. This research may serve as a guide to the optimization design of the relevant processes and dies.

Stress-state dependence of cavitation and flow behavior in superplastic aluminum alloys

A detailed and quantitative investigation of the stress-state dependence of superplastic cavitation in fine-grained aluminum alloys has been carried out to develop clear evidentiary support to build future models. Several stress states, such as uniaxial tension, plane-strain tension, plane-strain compression, shear, and equibiaxial tension have been examined. Tests were carried out to large strain in an interrupted manner under a constant effective strain rate (\(\dot \varepsilon \)e) in the range of 10−4 to 10−2 s−1. Measurements of volume fraction, population density, and size distribution of cavities, made by image analysis via optical microscopy, show continuous emergence of new cavities as well as growth of cavities during superplastic straining. The total cavity volume fraction (V) increases exponentially with strain. The cavity growth rate, represented by η (equal to d ln V/dee), as well as the cavity population evolution rate with strain (dNc/dee, where Nc is the cavity number/unit area) are found to increase with normalized mean hydrostatic tensile stress (σm/ σe). An empirical equation for the biaxial forming limit in terms of the principal surface strains (e1 and e2) has been defined for a fixed cavity volume, as given by e1=a Vb − α e2, where a and b are constants determined from e1 values for plane strain (e2=0). The value of b is found to be 0.2 to 0.3, and α is 0.4 to 1.0.

Dynamic hardness measurements using a dropped ball: with application to 1018 steel

A practical method for measuring the hardness of metals at high strain rates (>103 s−1), using a dropped ball, is developed and demonstrated on cold-rolled plain carbon (1018) steel. The metal is assumed to be one-dimensional and rigid plastic. By formulating the problem in terms of the lateral, rather than the depth, dimensions of the indentation, the dynamic hardness can be obtained at load, obviating the need for rebound energy corrections. In addition, the Tabor strain equation relating to equivalent unidirectional compression is derived, and methods are also derived to include “piling-up” around indentations for plastic flow at constant volume. A previously unrecognized phenomenon that can occur in projectile indentation of metals, “ballistic strain softening”, is described. It is related to the fact that the dynamic hardness obtained by this test is a function of the ball radius times the strain rate divided by the strain. As a result, comparison of the dropped ball test flow stress data with those of constant strain rate tests requires a transform of the Tabor strain and strain rate data to constant strain rate conditions. When this is done, the dynamic yield stress data that are determined as a function of the effective strain rates agree with comparable published data for mild steel obtained using more conventional tests. The results also show that there is greatly enhanced strain hardening in irons and steels above a critical strain rate, which increases with purity. A dislocation model is used to explain this increase in terms of an additional dislocation generation mechanism coming into play.

One-Dimensional Consolidation Modeling Based on the Isotach Law for Normally Consolidated Clays

ABSTRACT A one-dimensional consolidation model of the isotach-law type is proposed for normally consolidated clays which have neither interparticle bonding nor sensitive structure. At first, the mechanical quantities that can absolutely define a consolidation state without employing any arbitrary reference satate are examined, and it is concluded that specific volume, f(=1+e), effective stress stress, σ', and natural strain rate, en, are best. Next, the existence of a single relationship f-σ'-en after compressional yielding is verified by the results obtained from various types of laboratory consolidation tests with the measurement of long-term secondary settlement. Then, a way of conceptualizing how to incorporate this relationship into the new consolidation models is introduced, and numerical simulations based on the new model are shown for clay layers of field-size. And finally, the simulation results are used to discuss the application limits of the Terzaghi theory.

Simple constitutive relationship for C–Mn steels deformed at elevated temperatures

The strain, strain rate and temperature dependence of a C-Mn steel (BS grade 430) deformed under plane strain compression conditions have been investigated in the temperature range 1173-1373 K, at strain rates of 0.25-25 s-1. It has been determined that the stress-strain behaviour of this material can be modelled satisfactorily in a rational manner by combining the exponential saturation law advanced by Sah et al., for description of the evolution of the flow stress, and modified appropriately to account for dynamic recrystallisation effects, with the kinetic models advanced by Kocks and Sellars-Tegart-Garofalo. The Kocks model has been introduced for description of the temperature and strain rate dependence of both the initial flow stress, at the beginning of plastic flow, and the apparent saturation stress, achieved at elevated strains. The Sellars-Tegart-Garofalo model has been employed for the description of the actual saturation stress, achieved after the work softening transient brought about by the operation of dynamic recrystallisation, also in terms of temperature and strain rate. The relaxation strain, in the Sah et al. law has been found to be dependent on the effective strain rate and it has been determined that such a dependency can be described by means of a simple parametric power law relationship. Also, it has been found that the optimised value for activation energy for deformation at elevated temperatures is very close to the activation energy of self-diffusion of iron in austenite, which emphasises the need to introduce into this kind of analysis scaling parameters as the temperature dependent shear modulus of the material. The stress-strain/strain rate/temperature relationship that has been developed in the present work is able to characterise satisfactorily both the flow stress and work hardening rate of the material under the deformation conditions explored, allowing a valid interpolation of the flow stress at any strain, temperature, and strain rate.

The effect of sequential tensile and cyclic torsion straining on work hardening of steel and brass

Plastic straining in metal forming often involves changes in the strain path, either in the process itself or in successive forming operations. This fact, however, is usually not taken into account in the analyses of forming processes, where the effective strain, temperature and strain rate are commonly considered as the sole process variables. In this paper, the effects of strain path changes on the work hardening behavior of low carbon steel and brass have been investigated under sequential tension and cyclic torsion. Both materials developed saturation flow stresses in pure cyclic torsion. Double stage experiments showed different hardening behaviors according to the deformation sequence and the material. The results were compared to those previously obtained for monotonic tensile and torsion tests.

Effects of nanocrystalline and ultrafine grain sizes on constitutive behavior and shear bands in iron

The mechanical behaviors of consolidated iron with average grain sizes from tens of nanometers to tens of microns have been systematically studied under uniaxial compression over a wide range of strain rates. In addition to the well-known strengthening due to grain size refinement, grain size dependence is observed for several other key properties of plastic deformation. In contrast with conventional coarse-grained Fe, high-strength nanocrystalline and submicron-grained Fe exhibit diminished effective strain rate sensitivity of the flow stress. The observed reduction in effective rate sensitivity is shown to be a natural consequence of low-temperature plastic deformation mechanisms in bcc metals through the application of a constitutive model for the behavior of bcc Fe in this strain rate and temperature regime. The deformation mode also changes, with shear localization replacing uniform deformation as the dominant deformation mode from the onset of plastic deformation at both low and high strain rates. The evolution and multiplication of shear bands have been monitored as a function of plastic strain. The grain size dependence is discussed with respect to possible enhanced propensity for plastic instabilities at small grain sizes.

Passive Mixing Control via Lobed Injectors in High-Speed Flow

The near-e eld e ow and mixing characteristics of nonreactive lobed fuel injectors in subsonic and transonic airstreams were studied experimentally. Three alternative injector geometries were explored, two of which had lobed shapes. These lobed injectors mixed gas-phase injectant (nitrogen) and coe owing air to different extents, straining e uid interfaces due to streamwise vorticity generation. The experiments were conducted in a “ trisonic” wind tunnel, with coe owing airstream Mach numbers ranging from 0.4 to 1.2. Visualization of the downstream evolution of the injectant was achieved via planar laser-induced e uorescence imaging of acetone seeded in the nitrogen. Comparisons of near-e eld e ow evolution, mixing properties, and scalar dissipation and strain rates were made among different injectors for the different experimental e ow conditions. It was observed that lobed injector geometries produced greater near-e eld mixing as well as higher effective interfacial strain rates than nonlobed injectors in the subsonic (Mach 0.4) regime, although at higher subsonic Mach numbers mixing increases were accompanied by a reduction in the effective strain rate. Flow evolution observed in the experiments was also compared with numerical simulations of vorticity evolution and rollup, with good correspondence.

Hexahedral mesh generation for remeshing in three-dimensional metal forming analyses

It is well known that the quality and efficiency of the design of metal forming processes can be significantly improved with the aid of effective numerical simulations. However, one of the prominent features in metal forming analysis using the finite element method is that the initial simple workpiece geometry becomes severely distorted by material flow, causing mesh degeneration due to locally concentrated deformation. Thus, an effective remeshing scheme is needed to continue the analysis and obtain more accurate analysis results. In the present study, for remeshing in three-dimensional metal forming analyses, a hexahedral mesh generator was developed. It is based on the master grid approach and octree based refinement scheme to generate uniformly sized or locally refined hexahedral mesh system. In particular, for refined hexahedral mesh generation, a modified Laplacian smoothing scheme for preserving specified mesh density conditions is proposed. Also, for the specification of mesh density conditions, distributions of effective strain rate gradient and posteriori error values based on a Z 2 error estimator were used. In order to investigate the applicability of the developed hexahedral mesh generator for remeshing, several three-dimensional metal forming analyses were carried out. From this study, it is construed that the developed hexahedral mesh generator can be effectively used for using CAMP form in three-dimensional metal forming analyses.

The Effect of Ram Speed on Mechanical and Thermal Properties in ECAE Process Simulation

Mechanical and thermal properties during equal channel angular extrusion (ECAE) process are analyzed by finite volume method simulation. Chronological effective strain behavior during ECAE was visualized by 3-dimensional simulation. Local instability during ECAE was detected by the detailed analyses (named as ‘center-divided points’ and ‘cut-area points’), which are indicative of effective strain, effective stress, effective strain rate and temperature. Different ram speed caused different heat dissipation history and accordingly different mechanical and thermal properties during ECAE. In this simulation work, most of deformation occurred at the slip plane agreeing with theoretical prediction.

Micro Damage Evolution Analysis of Target Impacted by Projectile.

A new dynamic stress-strain rate type constitutive model for mixed hardening material has been developed using evolutional Gurson type yield function for solving problems of rigid plastic porous materials. During the plastic process of ductile materials in many engineering problems, the failure of materials is mainly induced by the damage behaviors such as the nucleation of micro void, their evolutions and the coalescence. With the aid of some concept of parameters and formulations, such as generalized triaxiality function in stress space, void fraction, effective stress with micro void interaction and void induced effective strain rate, generalized triaxiality ratio and so on, the dynamic void evolutional process of mixed hardening material has been analyzed in detail. Based on the above constitutive law the rigid-plastic finite element modeling and the FEM computer system including the damage evolutional process have been developed. The micro damage phenomena caused by collision of a flying projectile on to a target is simulated in order to reveal the applicability of the method. The inherent relations between the penetration and perforation process, and damage evolution process during the impact of target plate by projectile are revealed.

A rigid–plastic hybrid element method for simulations of metal forming

In the present study, the rigid–plastic hybrid element method (HEM) is developed. The rigid–plastic HEM is a mixed approach of the rigid–plastic domain-BEM and the rigid–plastic FEM. Since the compatibilities of velocity as well as velocity’s derivative can be satisfied, the velocity and the derivative of the velocity can be calculated with the same precision with the rigid–plastic HEM. On the other hand, the conventional rigid–plastic FEMs are formulated with single variable (velocity), the velocity and the derivative of the velocity cannot be calculated with the same precision for the rigid–plastic FEMs. A plane strain forging problem is analyzed by the rigid–plastic HEM. Velocity fields and contours of effective strain rate, effective strain, effective stress and shear stress, etc. can be obtained successfully.

Size-dependent hardness in annealed and work hardened α-brass and aluminum polycrystalline materials using activation volume analysis

A study of the size-dependent hardness in aluminum and α-brass is presented. The study employs rate-effects to examine the fundamental mechanisms responsible for the indentation hardness size dependence (effect), or (ISE). These rate effects are characterized in terms of the rate sensitivity of the hardness, ∂ H/∂ln ε eff, where H is the hardness and ε eff is an effective strain rate in the plastic zone beneath the indenter. ∂ H/∂ln ε eff is measured using indentation creep, load relaxation, and rate change experiments. ∂ H/∂ln ε eff is used to calculate the activation volume, V*; activation volume data measured using conventional uniaxial testing are compared with activation volume data measured using nanoindentation. The data for α-brass when plotted V* vs. H (hardness) or σ (flow stress), extrapolated into literature data from conventional uniaxial testing, while the aluminum data suffered an offset. We propose some mechanisms for this offset. Using V* formalism, we demonstrate using materials with different stacking fault energy (SFE) and specimens with different levels of work hardening how increasing the dislocation density affects V*; these effects may be taken as a kinetic signature of dislocation strengthening mechanisms. We depicted an ISE in both H and ∂ H/∂ln ε eff( V*). The trend of V*-vs.- H as a result of the ISE is consistent with the trend of testing specimens with different levels of work hardening. This indicates that a dislocation mechanism drives the ISE.

Nanoindentation and the indentation size effect: Kinetics of deformation and strain gradient plasticity

A study of the indentation size effect (ISE) in aluminum and alpha brass is presented. The study employs rate effects to examine the fundamental mechanisms responsible for the ISE. These rate effects are characterized in terms of the rate sensitivity of the hardness, ∂H/ ∂ ln ε ̇ eff , where H is the hardness and ε ̇ eff is an effective strain rate in the plastic volume beneath the indenter. ∂H/ ∂ ln ε ̇ eff can be measured using indentation creep, load relaxation, or rate change experiments. The activation volume V ∗ , calculated based on ∂H/ ∂ ln ε ̇ eff which can traditionally be used to compare rate sensitivity data from a hardness test to conventional uniaxial testing, is calculated. Using materials with different stacking fault energy and specimens with different levels of work hardening, we demonstrate how increasing the dislocation density affects V ∗ ; these effects may be taken as a kinetic signature of dislocation strengthening mechanisms. We noticed both H and ∂H/ ∂ ln ε ̇ eff (V ∗) exhibit an ISE. The course of V ∗ vs. H as a result of the ISE is consistent with the course of testing specimens with different level of work hardening. This result was observed in both materials. This suggests that a dislocation mechanism is responsible for the ISE. When the results are fitted to a strain gradient plasticity model, the data at deep indents (microhardness and large nanoindentation) exhibit a straight-line behavior closely identical to literature data. However, for shallow indents (nanoindentation data), the slope of the line severely changes, decreasing by a factor of 10, resulting in a “bilinear behavior”.

From the basic mechanics of orthogonal metal cutting toward the identification of the constitutive equation

This paper proposes a methodology to identify the material coefficients of constitutive equation within the practical range of stress, strain, strain rate, and temperature encountered in metal cutting. This methodology is based on analytical modeling of the orthogonal cutting process in conjunction with orthogonal cutting experiments. The basic mechanics governing the primary shear zone have been re-evaluated for continuous chip formation process. The stress, strain, strain rate and temperature fields have been theoretically derived leading to the expressions of the effective stress, strain, strain rate, and temperature on the main shear plane. Orthogonal cutting experiments with different cutting conditions provide an evaluation of theses physical quantities. Applying the least-square approximation techniques to the resulting values yields an estimation of the material coefficients of the constitutive equation. This methodology has been applied for different materials. The good agreement between the resulting models and those obtained using the compressive split Hopkinson bar (CSHB), where available, demonstrates the effectiveness of this methodology.

Finite element simulation of die design for hot extrusion process of Al/Cu clad composite and its experimental investigation

A clad composite material is a variant of the typical composites which is composed of two or more materials joined at their interface surface. The advantage of clad material is that the combination of different properties of materials can satisfy both the need of good mechanical properties and the demand of user such as electrical properties simultaneously. This paper is concerned with the direct and indirect extrusion process of copper-clad aluminum rod. Extrusion of copper-clad aluminum rod was simulated using a commercially available finite element package, DEFORM which can be used to simulate metal forming and heat transfer, welding and machining processes. The simulations were performed for copper-clad aluminum rod to predict the distributions of temperature, effective stress, effective strain rate and mean stress for various sheath thickness, die exit diameters and die temperatures. From the simulations, it was found that the larger the die outlet diameter and the thickness of the sheath material are, the better results can be acquired. It was found that the experimental result for lubricant material with carbon oil has good agreement with extrusion force from finite element analysis.

Comparative study of a high-strain-rate superplastic Al-4.4Cu-1.5Mg/21SiCW sheet under uniaxial and equibiaxial tension

In this paper, the strain rate sensitivity exponent and the cavitation behavior of a high-strain-rate superplastic Al-4.4Cu-1.5Mg/21SiCW sheet were examined under uniaxial and equibiaxial tension at the optimal temperature of 793 K. A maximum elongation of about 335% was obtained at the initial strain rate of 0.17 s−1. It was found that the strain rate sensitivity of the composite under uniaxial and equibiaxial tension was 0.34 and 0.36, respectively. The reasons for a large discrepancy between uniaxial and equibiaxial stress versus strain rate curves were analyzed. It was concluded that the flow stress–strain rate relationship determined from uniaxial tension could be used for forming processes subject to complex stress states after proper adjustment. The amount of cavity was found to increase with increasing strain and the amount of cavity obtained under equibiaxial tension was slightly larger than that under uniaxial tension at the same effective strain rate. A slightly higher cavity growth rate parameter was also observed under equibiaxial tension. The experimental results revealed that the cavity growth was essentially plastic-controlled. It was suggested that the presence of liquid phase was beneficial to nucleation at the interfaces and limited the cavity growth rate.

Low cycle fatigue behavior of Ti alloy IMI 834 at room temperature

Low cycle fatigue behavior of the Ti alloy IMI 834 was studied, for a bimodal microstructure with ≈14 vol.% primary α (αp) in the matrix of transformed β, at different total strain amplitudes (Δεt/2) from ±0.75 to ±1.7%, at room temperature. TEM examination revealed silicide particles at the interface of secondary α platelets in the transformed β, at the boundary of αp and transformed β, and extremely fine precipitates of ordered Ti3Al in the matrix. Cyclic softening was observed at all the above strain amplitudes. However, the degree as well as the rate of softening increased markedly at Δεt/2⩾1%. Cyclic softening was much less at low strain amplitude (Δεt/2⩽0.8%). The increase in the degree and the rate of softening at higher strain amplitudes is associated with increase in the number and more complete shearing of the ordered Ti3Al precipitates, from increase in the number of slip bands and glide dislocations. The increase in the number of glide dislocations in each cycle, with increase in strain amplitude occurs from increase in the effective strain rate to maintain the cyclic frequency at constant level. Bi-linearity was observed in the Coffin–Manson relationship and it was found to be associated with change in the deformation behavior from low to high strain amplitude.

Research on the flow stress characteristics of AISI 1006 and AISI 5140 in the temperature range of warm forging by means of thermo-mechanical experiments

The flow stress is one of the most essential parameters that reflect the capability of a material in plastic deformation. It is also an important factor that affects the precision of finite element (FE) simulation. However, recent research on material flow stress has focused mainly on cold and hot forging: as to warm forging, little research has been done on this aspect. With the gradually widening use of warm forging technology in precision plastic forming, the determining of the material flow stress systematically and accurately becomes the basis of further research on material plastic deformation. In this paper, the changing rule of the flow stress of AISI 1006 and AISI 5140 in the temperature range of warm forging has been analyzed systematically through thermo-mechanical experiments. The research considers sufficiently the influence of forming temperature, effective strain and strain rate. The experimental results offer a solid theoretical basis for the foundation of a mathematical model of flow stress, FEM simulation, for the calculation of the forming load, and for the working-out of the forming process.

Rigid-plastic meso-damage constitutive theory for porous composites reinforced by particles

This paper is aimed at the construction of rigid-plastic meso-damage constitutive theory for porous composites reinforced by rigid particles. In order to overcome the obstacles to establishing rigid-plastic theory, a few concepts, such as the effective stress, effective strain rate, nominal effective stress, nominal effective strain rate, generalized triaxiality ratio and generalized triaxiality function, are defined. In addition, exact mathematical transformations that relate to the physical quantities in stress space and strain rate space are developed. The physical meanings of the concepts introduced in the theory are systematically annotated. The potentiality to predict and control the strength and ductility of particle reinforced porous composites by applying the constitutive theory is revealed.