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 21 10 s to 61 10 s (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

Modelling ricochet of a cylinder on water using ALE and SPH methods

The ricochet means the rebound off a surface and is a very important scenario in engineering applications. The specific case of an impact of a solid steel body on a water surface has been chosen for the ricochet example. This solid body hits the water surface with a certain velocity and angle and their dependency on the ricochet behaviour is of interest. This impact scenario can be further developed for more complex impact scenarios, like the ditching of aeroplanes, and has been extensively studied in the past. Due to that fact, it was decided to compare the two numerical analyses with each other; SPH in the internal developed code MCM at Cranfield University with the ALE method in the commercial programme LS-Dyna. The early state of the development was the reason that a 2D model was developed in the 3D solver and therefore verification with another method crucial. Therefore the two simulations were set up and the ricochet behaviour investigated. In contrast to the experimental results, these results demonstrate that independent of the numerical method, both models show an unexpected overproduction of ricochet at higher impact velocities, but agree in their over prediction. The benefits arising out of the collaborative approach of SPH and ALE to describe a problem are presented

On the dynamic tensile strength of Zirconium

Despite its fundamental nature, the process of dynamic tensile failure (spall) is poorly understood. Spall initiation via cracks, voids, etc, before subsequent coalesce, is known to be highly microstructure-dependant. In particular, the availability of slip planes and other methods of plastic deformation controls the onset (or lack thereof) of spall. While studies have been undertaken into the spall response of BCC and FCC materials, less attention has paid to the spall response of highly anisotropic HCP materials. Here the dynamic behaviour of zirconium is investigated via plate-impact experiments, with the aim of building on an ongoing in-house body of work investigating these highly complex materials. In particular, in this paper the effect of impact stress on spall in a commercially sourced Zr rod is considered, with apparent strain-rate softening highlighted

Development of a total Lagrangian SPH code for the simulation of solids under dynamic loading

This thesis makes use of an alternative SPH formulation, the Total Lagrangian formulation, to characterise dynamic events in solids and to achieve the proposed objectives outlined in Chapter 1. The structure is as follows: Chapter 1, Introduction, describes the motivation for this research and outlines the objectives and the structure of this thesis. Chapter 2, SPH fundamentals, supplies the standard procedure to generate particle equations and provides a comprehensive summary of gradient approximation formulae in SPH. The discretised SPH form of the conservation laws is included here. Chapter 3, SPH drawbacks: describes the limitations of SPH such as particle deficiency, consistency, zero energy modes, treatment of boundaries and the tensile instability problem. A rigorous stability analysis of continua and SPH particle equations is also presented in this chapter. Chapter 4, Total Lagrangian SPH. Continuum Mechanics considerations are discussed here; detailed derivations of SPH equations in a total Lagrangian framework are given together with potential corrections to the total Lagrangian SPH equations. Chapter 5, Total Lagrangian SPH algorithms and their implementation using FORTRAN. This chapter gives a brief introduction to explicit codes. It also provides flow charts describing the Total Lagrangian algorithms and their integration into the MCM code. Chapter 6, Total Lagrangian SPH code validation. This chapter includes problems of varying degrees of complexity. Examples are provided to illustrate how the Total Lagrangian SPH code compares to a conventional collocational SPH code. Cases are supplied for which the analytical solution is known, and the results compared with the SPH approximations in order to show the accuracy of the approximation. Some examples are supplied which provide a direct comparison between SPH and non linear FE results and SPH and experimental results. Chapter 7, Alternative formulation of SPH equations and improvements to the standard MCM code: Various modifications to the standard SPH code are presented. These modifications include the implementation of subroutines that make use of an alternative approach to ensure the conservation of mass law is met locally at every particle. The introduction of XSPH to achieve further stabilisation of the code was also carried out and some examples are provided. The theory behind an alternative form of the conservation of mass equation as proposed by Belytschko [4] is explained and its implementation into the SPH code is assessed through examples. Also, an alternative formulation of SPH equations based on the general theory of mixed Lagrangian-Eulerian formulations [35] is presented: these equations could serve as the foundation for future research in this field. Chapter 8, Conclusions are presented in this chapter. A brief literature review is provided at the beginning of each chapter as a means of introduction to the topic and a concise summary outlines the main points discussed.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Numerical modelling of the effect of using multi-explosives on the explosive forming of steel cones

Modelling and analysis of underwater explosive forming process by using FEM and SPH formulation is presented in this work. The explosive forming of a steel cone is studied. The model setup includes a low carbon steel plate, plate holder, forming die as well as water and C4 explosive. The effect of multiple explosives on rate of targets deformation has been studied. Four different multi-explosives models have been developed and compared to the single explosive model. The formability of the steel plate based on forming limit failure criteria has been investigated. Aspects such as shape of plates deformation and thickness of the plate during the forming process have been examined. The model results indicate that a multi-explosives model does not always guarantee a faster rate of target deformation without central explosive. On the other hand the model results indicate that the multi-explosives setup is capable of preventing crack failure of the steel plate during the forming process which would occur if a single explosive model was used

Transport Theorem for Spaces and Subspaces of Arbitrary Dimensions

Copyright © 2020 by the authors. Using the apparatus of traditional differential geometry, the transport theorem is derived for the general case of a M-dimensional domain moving in a N-dimensional space, . The interesting concepts of curvatures and normals are illustrated with well-known examples of lines, surfaces and volumes. The special cases where either the space or the moving subdomain are material are discussed. Then, the transport at hypersurfaces of discontinuity is considered. Finally, the general local balance equations for continuum of arbitrary dimensions with discontinuities are derived

A study of the effect of projectile orientation on the results of ballistic impact tests as described in the EASA CS-25 regulations for fuel tank access covers

This paper presents the results of an investigation of the ballistic limits and failure modes of AA2024-T351 sheets impacted with cubical projectiles. The experiment/test setup was based on EASA CS-25 regulations for fuel tank access covers. The effect of cube orientation on the ballistic limit and failure modes was considered in detail. A 25% variation in ballistic limit was observed with the lowest ballistic limit (202 m/s) observed for the cubical projectile edge impacted on the target. In the cube face impacts, the ballistic limit was higher (223 m/s), and the highest ballistic limit (254 m/s) was observed for the corner impact. The observed differences in the ballistic limit were due to differences in failure mechanism, which resulted in different localised deformations near the projectile impact point, but also led to differences in global dishing deformation

Synergistic effect of hybrid reinforcement on magnesium-based composites for enriching mechanical and tribological characteristics

Supplementary material is available online at: https://journals.sagepub.com/doi/10.1177/09544089231221683#supplementary-materials .The exceptional mechanical, microstructural, and tribological characteristics of friction stir processed (FSP) hybrid and mono nanocomposite materials resulted in growing research interest. In the presented work, the base matrix of magnesium-based AZ31B alloy was reinforced with fly ash (FA) and nano-titanium carbide (n-TiC) particulates using FSP and resulting in both hybrid and mono composite surfaces. The microstructures and homogeneous distribution of reinforcing particulates of the synthesized composites were investigated with optical microscopy (OM) and field emission scanning electron microscopy (FESEM). In addition, for the synthesized nanocomposites, mechanical and tribological characteristics were investigated including using tensile and compression strength, micro/nano-hardness, and wear characteristics. The OM and FESEM data indicate that owing to the significant impact of the FSP process, grain refinement and the homogenous dispersion of the FA and n-TiC nanoparticles for both mono and hybrid composites were achieved. Overall, the new nano-hybrid composites have better mechanical properties due to improved interfacial bonding and homogeneous dispersion of hybridized n-TiC/FA reinforcements. The results indicate that the AZ31B/FA/TiC hybrid nanocomposite has better mechanical and tribological characteristics than the base alloy and the mono composite materials. More specifically, the grain size was reduced nearly 20 times, microhardness was 1.72 times higher, ultimate tensile strength was 2.42 times higher, compressive strength was 2.57 times higher, and wear rate was, about 80% higher when contrasted to the base alloy. Lastly, it is expected that this composite can offer a remarkable solution for crafting high-performance automotive parts.The authors received no financial support for the research, authorship, and/or publication of this article

Modelling of Strain Softening Materials Based on Equivalent Damage Force

The main aim of the work presented in this paper was addressing localisation problem observed in the analysis of strain softening materials using finite element methods (FEM) combined with local continuum damage mechanics (CDM) approach. Strain softening is typically observed in damaged quasi brittle materials such as fibre reinforced composites and application of the CDM approach with the classic FEM features a number of anomalies, including mathematical (change of the type of partial differential equations leading to ill-posed boundary value problem), numerical (pronounced mesh dependency) and physical (infinitely small softening zone with the zero dissipated energy). These features of the classic FEM solutions have been already demonstrated in (Vignjevic, Djordjevic et al. 2014). The model proposed here is still based on the local CDM approach, but introduces an alternative definition of damage effects in the system of equilibrium equations. The constitutive equation in the model is defined in terms of effective stress, whilst the damage effects in the conservation of momentum equation are calculated as equivalent damage force (EDF), which contributes to the equilibrium on the right hand side of the momentum equation. The main advantages of this model are that the problem remains well posed, as the type of partial differential equations remains unchanged when the material enters softening, numerical stability, which is preserved without a need for regularisation measures, and significantly reduced mesh dependency. In addition, the EDF model can be combined with existing local CDM damage evolution functions and does not violate symmetry of the stiffness tensor. The EDF model was implemented in in-house developed coupled FEM - MCM code, where explicit FEM (Liu 2004) is coupled with a stable TotalLagrange form of SPH (Vignjevic, Reveles et al. 2006, Vignjevic, Campbell et al. 2009). Its performance is demonstrated in the analysis of a dynamic one dimensional stress wave propagation problem, which was analytically solved in (Bazant, Belytschko 1985). For a range of loading rates that correspond to the material softening regime, the numerical results shown nonlocal character with a finite size of the damaged zone, controlled with the damage characteristic length, which can be experimentally determined and is an input parameter independent of the discretisation density.European Commissio