Hypervelocity impacts on thin brittle targets: Experimental data and SPH simulations

The meteoroids and debris environment play an important role in the reduction of spacecraft lifetime. Ejecta or secondary debris, are produced when a debris or a meteoroid impact a spacecraft surface. Brittle materials are particularly sensitive to HVI in term of damages and amount of ejected matter: the ejected fragments total mass is in the order of 100 times bigger than the impacting mass. The French atomic energy commission (CEA) faces the same problem in the Laser MégaJoule project. The lasers optics will be bombarded by hypervelocity debris and shrapnel resulting from target disassembly. Two millimeter thick fused silica disposable debris shields (DDS) located in front of the main debris shields might be used to reduce very small shrapnel cratering on the main debris shields. The aim of this paper is to study the damaging and ejection processes that occur during HVI on thin brittle targets. A two-stage light-gas gun has been used to impact 2 mm DDS with 500 μm steel projectiles. Experimental characterization of ejected matter has also been performed: lightweight paperboards coated with adhesive have been used to collect ejected fragments including spalls. Numerical simulation using the smooth particle hydrodynamics (SPH) method of LS-DYNA and the Johnson Holmquist material model were performed. The results of these calculations are compared to experimental data which include the damage features in the targets (spalled zones and perforation hole) and the ejection clouds. Satisfying agreement between numerical and experimental simulations was obtained for damage characteristics and ejection phenomena.     

Creep failure model of a tempered martensitic stainless steel integrating multiple deformation and damage mechanisms

A new model considering both deformation and damage evolution under multiple viscoplastic mechanisms is used to represent high temperature creep deformation and damage of a martensitic stainless steel in a wide range of load levels. First, an experimental database is built to characterise both creep flow and damage behaviour using tests on various kinds of specimens. The parameters of the model are fitted to the results and to literature data for long term creep exposure. An attempt is made to use the model to predict creep time to failure up to 10⁵ h.     

A model of continuum damage mechanics for fatigue failure

This paper describes the development of a generalized model of continuum damage mechanics for fatigue fracture. With the introduction of a new damage effect tensor, the necessary constitutive equations of elasticity and plasticity coupled with damage are for the first instance derived. This is followed by the formulations of fatigue damage dissipative potential function and a fatigue damage criterion which are required for the development of a fatigue damage evolution equation. The fatigue evolution model is based on the hypothesis that the overall fatigue damage is induced by the summation of elastic and plastic damages.The validity of the damage model proposed is verified by comparing the predicted and measured number of cycles to failure for ten tensile specimens each applied with different load ranges and excellent agreement has been achieved.University of Science and Technology of China     

A synergistic creep fatigue failure model damage (case of the alloy Z5NCTA at 550 °C)

Creep-fatigue tests have been performed on nickel base alloy Z5NCTA 33-21 grade 1. Hold time varied from 0, 10, 30, 90, 300, 1440 and 10,080 min at two values of strain range. It was found that the number of cycles to failure N_R decreases with holding time t_m, according to a power law:

N_R=1.88×10³·(t_m)^-0.39.     

A composite ply failure model based on continuum damage mechanics

A material model including the failure behaviour is derived for a thin unidirectional (UD) composite ply. The model is derived within a thermodynamic framework and the failure behaviour is modelled using continuum damage mechanics. The following features describe the model: (i) The ply is assumed to be in a plane state of stress. (ii) Three damage variables associated with the stress in the fibre-, transverse and shear directions, respectively, are used. (iii) The plastic behaviour of the matrix material is modelled. (iv) The difference in the material response in tensile and compressive loading is modelled. (v) Rate dependent behavior of plasticity and damage (i.e. strength) is modelled.     

A combined elastoplastic damage model for progressive failure analysis of composite materials and structures

The paper is concerned with the development and verification of a combined elastoplastic damage model for the progressive failure analysis of composite materials and structures. The model accounts for the irreversible strains caused by plasticity effects and material properties degradation due to the damage initiation and development. The strain-driven implicit integration procedure is developed using equations of continuum damage mechanics, plasticity theory and includes the return mapping algorithm. A tangent operator consistent with the integration procedure is derived to ensure a computational efficiency of the Newton–Raphson method in the finite element analysis. The algorithm is implemented in Abaqus as a user-defined subroutine. The efficiency of the constitutive model and computational procedure is demonstrated using the analysis of the progressive failure of composite laminates containing through holes and subjected to in-plane uniaxial tensile loading. It has been shown that the predicted results agree well with the experimental data reported in the literature.     

带有限等待的动态HFS调度的拉格朗日松弛算法

作为基于最优化的近似算法,分析了拉格朗日松弛算法的分解策略,设计了算法的实现优化过程.针对从钢铁生产提炼出的带有限等待时间要求的动态HFS调度,采用基于工件解耦的分解策略,应用拉格朗日松弛算法进行求解,以最小化总加权完成时间和工件等待惩罚之和.该算法将工件耦合约束松弛到目标函数中,将形成的松弛问题分解成多个更易求解的工件级子问题,进而利用动态规划求解这些子问题,通过拉格朗日乘子的更新迭代过程获得原问题的近优解.对不同问题规模的测试结果表明,该算法能在较短的计算时间内得到较好的近优解,说明了拉格朗日松弛算法求解等待时间受限的HFS调度的可行性和有效性.     

Numerical simulations of void linkage in model materials using a nonlocal ductile damage approximation

Experiments on the growth and linkage of 10 μm diameter holes laser drilled in high precision patterns into Al-plates were modelled with finite elements. The simulations used geometries identical to those of the experiments and incorporated ductile damage by element removal under the control of a ductile damage indicator based on the micromechanical studies of Rice and Tracey. A regularization of the problem was achieved through an integral-type nonlocal model based on the smoothing of the rate of a damage indicator D over a characteristic length L. The simulation does not predict the experimentally observed damage acceleration either in the case where no damage is included or when only a local damage model is used. However, the full three-dimensional simulations based on the nonlocal damage methodology do predict both the failure path and the failure strain at void linkage for almost all configurations studied. For the cases considered the critical parameter controlling the local deformations at void linkage was found to be the ratio between hole diameter and hole spacing.     

A progressive failure model for mesh-size-independent FE analysis of composite laminates subject to low-velocity impact damage

An original, ply-level, computationally efficient, three-dimensional (3D) composite damage model is presented in this paper, which is applicable to predicting the low velocity impact response of unidirectional (UD) PMC laminates. The proposed model is implemented into the Finite Element (FE) code ABAQUS/Explicit for one-integration point solid elements and validated against low velocity impact experimental results.     

A molecular dynamics approach in simulations of fluid-solid particles flow

In the paper a discrete system of particles carried by fluid is considered in a planar motion. The volumetric density of particles is assumed to be small enough such that they can be treated within the framework of a molecular dynamics model. The fluid is then considered as a carrier of particles. The Landau-Lifshitz concept of turbulence is used to describe the fluctuating part of fluid velocity. This approach is applied to simulate different regimes (laminar and turbulent) and various states of particle motion (moving bed, heterogeneous flow, and homogeneous flow) using only two parameters, which have to be determined experimentally. These two parameters, found for a particular pipe and for a particular velocity from a simple experiment, then can be used for other pipe diameters and different velocities. The computer simulations performed for the flow of particles in pipes at different flow velocities and different pipe diameters agree favorably with experimental observations of the type of flow and critical velocities identifying transitions from one type to another. Received: 8 January 1999     

Structural damage identification: influence of model incompleteness and errors

This paper presents a study of the influence of model incompleteness and errors in a structural damage identification technique based on modal data, leading to a set of linear equations. To deal with the incompleteness three methods are used: (1) dynamic and (2) static expansions of measured degrees of freedom and (3) replacement of unmeasured degrees of freedom by their undamaged counterparts. These methods are applied on damage identification of a laminated rectangular plate. The numerical tests show that the best accuracy is obtained with the dynamic expansion, followed by the static expansion and finally, the replacement of unmeasured degrees of freedom. It is also demonstrated that for small damage the errors are the main influence, whereas for large damage the incompleteness becomes the most important factor in the results. The identification of small and large damages is performed by deleting non-reliable equations, i.e., equations that contain large errors.     

A fatigue damage model of composite materials

The mechanical properties of composite materials degrade progressively with the increasing of the number of cyclic loadings. Based on the stiffness degradation rule of composites, a phenomenological fatigue damage model is presented in this paper, which contains two material parameters. They are proportional to the fatigue life of materials and inversely proportional to the fatigue loading level. Thirteen sets of experimental data of composite stiffness degradation were employed to verify the presented model, and the statistical results showed that this model is capable of describing the damage evolution of composite materials. The characteristics of damage development and accumulation of composite materials subjected to variable loading were studied in this paper. Four sets of two-level loading experimental data were cited to verify the damage model, and the results showed that the predicted life is in good agreement with the experimental ones.     

A heat exchanger model for mixtures and pure refrigerant cycle simulations

This paper describes a heat exchanger simulation developed for transient and steady state cycle simulations of mixtures and pure components. The simulation focuses on air to refrigerant condensers and evaporators found in residential heat pumps. The refrigerant differential momentum, continuity, species and energy equations are solved for these components and the steady state results are verified experimentally. Ten different heat transfer correlations for condensation and evaporation are evaluated to determine which best reproduces experimental data. Of those tested Jung and Radermacher's (1989, Int. J. Heat Mass Transfer32 2435–2446) heat transfer correlation worked the best for evaporation while Dobson et al.'s (1994, ACRC Project 37) correlation worked the best for condensation. The experimentally determined capacity of four cross flow heat exchangers operating as condensers and evaporators with four different refrigerants is compared to the simulation results. The capacities predicted by the simulation agreed with the experimental results within ±8.0%. Furthermore, the simulation is used to quantify the effects of using a zeotropic mixture, R-407C, with cross, parallel and counter flow heat exchangers. As compared to a typical cross flow heat exchanger at typical heat pump operating conditions, the simulation predits that a pure parallel flow heat exchanger can decrease capacity by as much as 8.3% while a pure counter flow heat exchanger can increase performance by up to 4.4%.     

Analytical study for the estimation of thermal properties of processed meat based on hyperbolic heat conduction model

This study proposes an analytical method in conjunction with existing experimental temperature to estimate the unknown relaxation time and thermal diffusivity of processed meat based on the hyperbolic heat conduction model. This analytical method is a combination of the Laplace transform and least squares methods. The thermal contact resistance at the interface between adjacent samples at different temperatures is assumed to be negligible. The relaxation time is estimated from the temperature jump at a specific measurement location. The thermal diffusivity is determined from the definition of the dimensionless spatial coordinate and the resulting relaxation time. The results show that the relaxation time and thermal diffusivity obtained are in good agreement with the existing results. The obtained dimensionless temperature history at a specific measurement location is close to the experimental temperature data. This means that the Cattaneo–Vernottee (CV) model can be suitable for this study. The proposed analytical inverse method can be applied to determine a more accurate estimate of such problems. A comparison of the estimate obtained from CV and dual phase lag models is made.     

Computer simulations reveal complex distribution of haemodynamic forces in a mouse retina model of angiogenesis

There is currently limited understanding of the role played by haemodynamic forces on the processes governing vascular development. One of many obstacles to be overcome is being able to measure those forces, at the required resolution level, on vessels only a few micrometres thick. In this paper, we present an in silico method for the computation of the haemodynamic forces experienced by murine retinal vasculature (a widely used vascular development animal model) beyond what is measurable experimentally. Our results show that it is possible to reconstruct high-resolution three-dimensional geometrical models directly from samples of retinal vasculature and that the lattice-Boltzmann algorithm can be used to obtain accurate estimates of the haemodynamics in these domains. We generate flow models from samples obtained at postnatal days (P) 5 and 6. Our simulations show important differences between the flow patterns recovered in both cases, including observations of regression occurring in areas where wall shear stress (WSS) gradients exist. We propose two possible mechanisms to account for the observed increase in velocity and WSS between P5 and P6: (i) the measured reduction in typical vessel diameter between both time points and (ii) the reduction in network density triggered by the pruning process. The methodology developed herein is applicable to other biomedical domains where microvasculature can be imaged but experimental flow measurements are unavailable or difficult to obtain.     

A single-product network design model with lead time and safety stock considerations

Most existing network design and facility location models have focused on the trade-off between the fixed costs of locating facilities and variable transportation costs between facilities and customers. However, operational performance measures such as service levels and lead times are what motivates customers to bring business to a company and should be considered in the design of a distribution network. While some previous work has considered lead times and safety stocks separately, they are closely related in practice, since safety stocks are often set relative to the distribution of demand over the lead time. In this paper we consider a two-stage supply chain with a production facility that replenishes a single product at retailers. The objective is to locate Distribution Centers (DCs) in the network such that the sum of the location and inventory (pipeline and safety stock) costs is minimized. The replenishment lead time at the DCs depends on the volume of flow through the DC. We require the DCs to carry enough safety stock to maintain the prescribed service levels at the retailers they serve. The explicit modeling of the relationship between the flows in the network, lead times and safety stocks allows us to capture the trade-off between them. We develop a Lagrangian heuristic to obtain near-optimal solutions with reasonable computational requirements for large problem instances.     

A model of fatigue crack growth based on Dugdale model and damage accumulation

The modified Dugdale model given by Budiansky-Hutchinson and a Coffin-Manson type damage law are used to calculate the cumulative fatigue damage of material elements at the tip of a fatigue crack. From this analysis a fatigue crack growth equation is obtained which gives predicted crack growth rates in reasonable agreement with experimental data for two aluminium alloys 7075-T6 and 2024-T81, two titanium alloys Ti-8A1-1Mo-1V and Ti-6A1-6V and a PH13-8Mo stainless steel. Limitations of this new fatigue crack growth model are also discussed.