Mechanical Threshold Strength Research Articles

Mechanical Properties of Strengthening 5083-H111 Aluminum Alloy Plates at Elevated Temperatures

The use of aluminum alloys for external strengthening of reinforced concrete (RC) beams has been capturing research interest. Exposure to harsh environmental conditions can severely impact the strengthening efficiency. This works aims to investigate the degradation in the mechanical properties of aluminum alloy AA 5083 plates when exposed to temperatures ranging from 25 to 300 °C. Quasi-static Isothermal tensile experiments were conducted at different temperatures. It was observed from the experimental results that the yield strength remained constant in the temperature range of 25–150 °C before starting to drop beyond 150 °C, with a total reduction of ≈ 40% at 300 °C. The elastic modulus was temperature sensitive with about 25% reduction at 200 °C before experiencing a significant and pronounced reduction at 300 °C. The percentage drops in stiffness and yield strength at 300 °C were 62.8% and 38%, respectively. In addition, the Mechanical Threshold Strength Model (MTS) parameters were established to capture the yield strength temperature dependence. Two analytical models were developed based on the experimental results. Both models can reasonably predict the elastic modulus and yield strength of AA 5083 plates as a function of temperature. It was concluded that AA plates should be properly insulated when used as externally bonded reinforcement to strengthen RC beams.

Modeling and simulation framework for dynamic strain localization in elasto-viscoplastic metallic materials subject to large deformations

This paper describes a theoretical and computational framework for the treatment of adiabatic shear band formation in rate-sensitive polycrystalline metallic materials. From a computational perspective, accurate representation of strain localization behavior has been a long-standing challenge. In addition, the underlying physical mechanisms leading to the localization of plastic deformation are still not fully understood. The proposed framework is built around an enhanced-strain finite element formulation, designed to alleviate numerical pathologies known to arise in localization problems, by allowing a localization band of given finite width (weak discontinuity) to be embedded within individual elements. The mechanical threshold strength (MTS) model is used to represent the temperature and strain rate-dependent viscoplastic response of the material. This classical flow stress model employs an internal state variable to quantify the effect of dislocation structure evolution (work hardening and recovery). In light of growing evidence suggesting that the softening effect of dynamic recrystallization may play a significant role, alongside thermal softening, in the process of shear band formation and growth, a simple dynamic recrystallization model is proposed and cast within the context of the MTS model with the aid of the aforementioned internal state variable. An initiation criterion for shear localization in rate and temperature-sensitive materials is introduced and used in the present context of high-rate loading, where material rate-dependence is pronounced and substantial temperature increases are achieved due to the dissipative nature of viscoplastic processes. In addition, explicit time integration is adopted to facilitate treatment of the dynamic problems under consideration, where strain rates in excess of 104 s−1 are typically attained. Two series of experiments are conducted on AISI 316L stainless steel, employing the commonly used top-hat sample geometry and the Split-Hopkinson Pressure Bar dynamic test system. Axi-symmetric finite element simulation results are compared to cross-sectional micrographs of recovered samples and experimental load–displacement results, in order to examine the performance of the proposed framework and demonstrate its effectiveness in treating the initiation and growth of adiabatic shear banding in dynamically loaded metallic materials. These comparisons demonstrate that thermal softening alone is insufficient to induce shear localization behaviors observed in some materials, such as stainless steel, and support the hypothesis that dynamic recrystallization and/or other softening mechanisms play an essential role in this process.

Strain Rate Dependant Material Model for Orthotropic Metals

In manufacturing processes anisotropic metals are often exposed to the loading with high strain rates in the range from 102 s-1 to 106 s-1 (e.g. stamping, cold spraying and explosive forming). These types of loading often involve generation and propagation of shock waves within the material. The material behaviour under such a complex loading needs to be accurately modelled, in order to optimise the manufacturing process and achieve appropriate properties of the manufactured component.The presented research is related to development and validation of a thermodynamically consistent physically based constitutive model for metals under high rate loading. The model is capable of modelling damage, failure and formation and propagation of shock waves in anisotropic metals. The model has two main parts: the strength part which defines the material response to shear deformation and an equation of state (EOS) which defines the material response to isotropic volumetric deformation [1]. The constitutive model was implemented into the transient nonlinear finite element code DYNA3D [2] and our in house SPH code. Limited model validation was performed by simulating a number of high velocity material characterisation and validation impact tests.The new damage model was developed in the framework of configurational continuum mechanics and irreversible thermodynamics with internal state variables. The use of the multiplicative decomposition of deformation gradient makes the model applicable to arbitrary plastic and damage deformations.To account for the physical mechanisms of failure, the concept of thermally activated damage initially proposed by Tuller and Bucher [3], Klepaczko [4] was adopted as the basis for the new damage evolution model. This makes the proposed damage/failure model compatible with the Mechanical Threshold Strength (MTS) model Follansbee and Kocks [5], 1988; Chen and Gray [6] which was used to control evolution of flow stress during plastic deformation. In addition the constitutive model is coupled with a vector shock equation of state which allows for modelling of shock wave propagation in orthotropic the material.Parameters for the new constitutive model are typically derived on the basis of the tensile tests (performed over a range of temperatures and strain rates), plate impact tests and Taylor anvil tests.The model was applied to simulate explosively driven fragmentation, blast loading and cold spraying impacts.

Incrementally objective implicit integration of hypoelastic–viscoplastic constitutive equations based on the mechanical threshold strength model

The present paper focuses on the development of a fully implicit, incrementally objective integration algorithm for a hypoelastic formulation of \(J_{2}\)-viscoplasticity, which employs the mechanical threshold strength model to compute the material’s flow stress, taking into account its dependence on strain rate and temperature. Heat generation due to high-rate viscoplastic deformation is accounted for, assuming adiabatic conditions. The implementation of the algorithm is discussed, and its performance is assessed in the contexts of implicit and explicit dynamic finite element analysis, with the aid of example problems involving a wide range of loading rates. Computational results are compared to experimental data, showing very good agreement.

Modelling of dynamic behaviour of orthotropic metals including damage and failure

A physically based material model for metals, with elastic–plastic and damage/failure orthotropy is proposed in this paper. The model is defined within the frameworks of irreversible thermodynamics and configurational continuum mechanics and integrated in the isoclinic configuration. The use of the multiplicative decomposition of deformation gradient makes the model applicable to arbitrary plastic and damage deformations. To account for the physical mechanisms of failure, the concept of thermally activated damage initially proposed by Klepaczko (1990) was adopted as the basis for the new damage evolution model. This makes the proposed damage/failure model compatible with the Mechanical Threshold Strength (MTS) model (Follansbee and Kocks, 1988; Chen and Gray, 1996; Goto et al., 2000; Gray et al., 1999; Chen et al., 1998) which was used to control evolution of flow stress during plastic deformation. In addition the constitutive model is coupled with a shock equation of state which allows for modelling of shock wave propagation in the material. The new model was implemented in DYNA3D and our in-house non-linear transient SPH code, MCM (Meshless Continuum Mechanics).Parameters for the new constitutive model for AA7010 (a polycrystalline aluminium alloy, whose orthotropy is a consequence of grain morphology), were derived on the basis of the tensile tests and Taylor anvil tests. The tensile tests were performed for the range of temperatures between 223.15K and 413.15K, and strain rates between 6.4×10-4s-1 and 6.4×101s-1.The new model was validated in two stages. The first stage comprised a series of single element tests design to separately validate elasticity, plasticity and damage related parts of the model. The second stage comprised a series of numerical simulations of Taylor anvil and plate impact tests for AA7010 and comparison of the numerical results with the experimental data. The numerical results illustrate the ability of the new model to predict experimentally observed behaviour.

Modelling of dynamic damage and failure in aluminium alloys

A physically based damage and failure model, applicable to orthotropic metals is proposed in this paper. To account for the physical mechanisms of failure, the concept of thermally activated damage initially proposed by Klepaczko [1], has been adopted as the basis for the model. This assumption makes the proposed damage/failure model compatible with the Mechanical Threshold Strength (MTS) model [2–6], which was used within the overall constitutive model to describe material behaviour in the plastic regime. A shock equation of state [7] was coupled with the rest of the constitutive model to allow for modelling of shock wave propagation in the material. The new model was implemented in DYNA3D [8] and coupled with our in-house non-linear transient SPH code, MCM (Meshless Continuum Mechanics).Parameters for the new constitutive model, i.e. parameters for the plasticity model and the damage model, were derived on the basis of the uniaxial tensile tests and Taylor anvil tests. The subject of investigation is a polycrystalline aluminium alloy AA7010, whose orthotropy is a consequence of meso-scale phase distribution, or grain morphology. Tensile tests were performed for the range of temperatures between 223.15K and 473.15K, and strain rates between 6.4×10−4s−1 and 6.4×102s−1.In order to validate the new damage model, a numerical simulation of Taylor anvil tests has been performed for AA7010, using a single stage gas gun at velocity of 200m/s. The numerical analysis clearly demonstrates the ability of this new model to predict experimentally observed damage and failure.

Numerical simulation of the pressure ram forming process

The pressure ram forming (PRF™) process is simulated by implementing the mechanical threshold strength (MTS) model into ABAQUS finite element analysis software through a user material subroutine (UMAT). The predicted shape and thickness distribution of the PRF aluminium bottle and the force on the backing ram during forming are found to be in good agreement with measurements.

Mechanical behavior of δ-phase Pu–Ga alloys. Part II: Model verification and application

We validated the mechanical threshold strength (MTS) model, developed in Part I, with approximately 50 different experimental results from the literature for both yield strength and ultimate tensile strength on Pu–Ga alloys. One standard deviation of the differences between the model’s yield-strength predictions and the experiments was 7.5% of the measured yield strength. The model also worked well predicting the ultimate tensile strength (UTS) of the alloys with gallium concentrations of 1 wt% or greater, although the accuracy of the UTS predictions was not as good as for yield strength. After validating the model, we studied the effects of gallium concentration, grain size, iron and nickel content, and carbon concentration on the yield strength of Pu–Ga alloys. The gallium concentration affected the yield strength more than any other microstructural variable. The yield strength increased 50% between 1 at.% Ga and 5.4 at.% Ga alloying addition. The grain size also produced a measurable strengthening effect, typical of other face-centered cubic metals. The yield strength increased 15% with a reduction in grain size from 50 μm to 10 μm. Finally, we found that there were no observable yield-strength effects resulting from different amounts of iron, nickel, or carbon impurities.

Mechanical behavior of δ-phase Pu–Ga alloys. Part I: Constitutive model

We developed a constitutive model, based on the mechanical threshold strength (MTS) model reported by Follansbee and Kocks [P.S. Follansbee, U.F. Kocks, Acta Metall. 36 (1988) 81], to predict the stress/strain behavior of face-centered cubic (fcc) δ-stabilized plutonium–gallium (Pu–Ga) alloys. Input to the model is derived from our previous work on other fcc metals and published test data for Pu–Ga alloys. The model accounts for the effects of temperature, strain rate, grain size, and alloy content on the constitutive behavior. In Part I, we describe the development of the model and present all the pertinent equations and parameters. In Part II, we validate the model against existing literature data and demonstrate how the model is used to quantify the effects of test condition, grain size, alloy content, and impurity levels.