High strain rate behavior of 4-step 3D braided composites under compressive failure

The out-of-plane and in-plane compressive failure behavior of 4-step 3D braided composite materials was investigated at quasi-static and high strain rates. The out-of-plane and in-plane direction compressive tests at high strain rates from 800/s to 3,500/s were tested with the split Hopkinson pressure bar (SHPB) technique. The quasi-static compressive tests were conducted on a MTS 810.23 tester and compared with those at high strain rates. The comparisons indicate that the failure stress, failure strain and compressive stiffness both for out-of-plane and in-plane loading directions are rate sensitive. For example, the failure stress, failure strain and stiffness are 55.19 MPa, 6.70% and 1.35 GPa respectively as opposed to 145.00 MPa, 1.21% and 13.50 GPa respectively for strain rate of 2,500 s⁻¹ under in-plane compression. The 3D braided composites have higher values of failure stress and strain for out-of-plane than for in-plane compression at the same strain rate; however, the in-plane compression stiffness is higher than that of out-of-plane compression at high strain rates. The compressive failure mode of 3D braided composites in the out-of-plane direction is mainly shear failure at various strain rates, while for the in-plane direction it is mainly cracking of matrix.     

编织角和承载方向对三维四向编织复合材料动态压缩性能的影响

利用分离式霍普金森压杆（SHPB）装置对三维四向编织碳纤维增强树脂基复合材料的动态压缩性能进行了研究。通过对编织角为20°、30°和45°的试验件分别进行沿纵向、横向和厚度方向的动态压缩试验,得到材料在800~2 000/s应变率范围内的应力-应变曲线,并与准静态压缩试验结果进行对比,研究了应变率、压缩方向及编织角对材料极限强度和弹性模量的影响。结合高速摄影记录的动态压缩过程,进一步分析了不同情况下材料的破坏模式与破坏过程。结果表明：应变率越高,材料的极限强度和弹性模量越大,材料在受压的三个方向上均具有一定的应变率强化效应,且高应变率下表现出比准静态压缩时更明显的脆性;编织角的改变对材料在三个方向上的动态压缩性能均有影响,其中对纵向的影响最为明显;不同方向受压时材料的失效形式不同,且准静态和高应变率下的失效形式也有区别。     

Mechanical characterization and modeling of the deformation and failure of the highly crosslinked RTM6 epoxy resin

The nonlinear deformation and fracture of RTM6 epoxy resin is characterized as a function of strain rate and temperature under various loading conditions involving uniaxial tension, notched tension, uniaxial compression, torsion, and shear. The parameters of the hardening law depend on the strain-rate and temperature. The pressure-dependency and hardening law, as well as four different phenomenological failure criteria, are identified using a subset of the experimental results. Detailed fractography analysis provides insight into the competition between shear yielding and maximum principal stress driven brittle failure. The constitutive model and a stress-triaxiality dependent effective plastic strain based failure criterion are readily introduced in the standard version of Abaqus, without the need for coding user subroutines, and can thus be directly used as an input in multi-scale modeling of fibre-reinforced composite material. The model is successfully validated against data not used for the identification and through the full simulation of the crack propagation process in the V-notched beam shear test.     

Thermo-mechanical behaviors of 3-D braided composite material subject to high strain rate compressions under different temperatures

This article reports the compressive behaviors of 3-D braided basalt fiber tows/epoxy composite materials under the temperature range of 23–210°C with the strain-rate range of 1300–2300 s^?1. A split Hopkinson pressure bar apparatus with a heating device was designed to conduct the out-of-plane compression tests. It was found that compression modulus, specific energy absorption, and peak stress decreased with the elevated temperatures, while failure strain gradually increased with the elevated temperatures. Compression modulus and peak stress were more sensitive to the temperature effect, whereas failure strain and specific energy absorption were more easily affected by the strain rate effect. The plasticity can be divided into two types: (a) the platform-shape plasticity; or (b) the slope-shape plasticity. The experimental condition of 150°C with 1827 s^–1 was a dividing threshold to differentiate the compression-failure mode and the shear-failure mode. The authentic microstructural finite element analysis results revealed that the distribution and accumulation of the inelastic heat led to the development of shear bands. Braided reinforcement had an important influence on the damage characteristics. When the temperature was below T_g, the material underwent a significant temperature rise during failure. But above T_g, the temperature rise was relatively steady.     

Strain-rate-dependent failure criteria for composites

The objective of this study was to characterize the quasi-static and dynamic behavior of composite materials and develop/expand failure theories to describe static and dynamic failure under multi-axial states of stress. A unidirectional carbon/epoxy material was investigated. Multi-axial experiments were conducted at three strain rates, quasi-static, intermediate and high, 10⁻⁴, 1 and 180-400 s⁻¹, respectively, using off-axis specimens to produce stress states combining transverse normal and in-plane shear stresses. A Hopkinson bar apparatus and off-axis specimens loaded in this system were used for multi-axial characterization of the material at high strain rates. Stress-strain curves were obtained at the three strain rates mentioned. The measured strengths were evaluated based on classical failure criteria, (maximum stress, maximum strain, Tsai-Hill, Tsai-Wu, and failure mode based and partially interactive criteria (Hashin-Rotem, Sun, and Daniel). The latter (NU theory) is primarily applicable to interfiber/interlaminar failure for stress states including transverse normal and in-plane shear stresses. The NU theory was expressed in terms of three subcriteria and presented as a single normalized (master) failure envelope including strain rate effects. The NU theory was shown to be in excellent agreement with experimental results.     

考虑应变率影响的厚壁筒残余应力场分析

本文针对弹塑性拉压循环加卸载条件下，不同的应变率（１０－４－１０－２ｓ－１）变化，对高强钢（ＰＣｒＮｉ３ＭｏＶ）材料的屈服应力、应变硬化参数和反向屈服应力等参量的影响进行了实验研究，提出了便于理论计算的简化弹塑性本构模型，并假设拉屈服应力与压屈服应力的差值不随应变率的不同而发生变化，这一假定与实验结果相符合，且便于工程计算。针对厚壁筒自紧加工工艺的残余应力场分析问题，用本文提出的模型对厚壁筒在四种不同的应变率条件下进行自紧加工时残余应力场的变化及不同的自紧效果进行了详细的分析和比较，并提出了改进工艺过程和提高自紧效果的建设性意见。     

High strain-rate localization and failure of crystalline materials

A theoretical and a computational model are introduced to study the micromechanical high strain-rate failure mechanisms of shear-strain localization in monocrystalline fcc structures. A theoretical framework for a constitutive model for the dynamic finite plastic deformation of rate-dependent single fcc crystals is developed. The micromechanics of plastic flow are based on a high strain-rate single crystal plasticity model and a visco-plastic power law. The single crystal is subjected to far-field dynamic tensile strain-rates ranging from 100/s to 2000/s. An explicit finite-element model is introduced for the integration of the numerically stiff visco-plastic constitutive relations. The total deformation rate tensor is obtained by the central difference explicit integration of the equations of motion. The plastic deformation rate tensor is obtained from the solution of an initial-value nonlinear problem for the resolved shear stresses. In time intervals when the differential equations for the resolved shear stresses are not numerically stiff, the initial-value problem is integrated by the explicit fifth-order Runge-Kutta adaptive time-step method. In time domains where the propagated error grows and the time-step must be restricted due to stability requirements, which is an indication of numerical stiffness, the initial-value problem is integrated by an A-stable method. To correctly differentiate time-step reductions due to stability, from time-step reductions due to accuracy, a stiffness ratio is defined. The present analysis corroborates experimental observations that high strain-rate shear-strain localization, in rate-dependent crystals, is a function of thermal and geometrical softening, overall strain-rates, strain hardening, strain-rate hardening, and strain-rate sensitivity.     

Mechanical characterization of soft materials using high speed photography and split hopkinson pressure bar technique

High-speed photography in conjunction with the viscoelastic Split Hopkinson Pressure Bar (SHPB) technique was used to study soft material behavior under dynamic loading conditions. The real-time strains recorded using high speed photography were also used for validating the existing viscoelastic SHPB model. Polyurethane, sculpturing clay, sorbothane and bologna were tested as examples of soft materials. The dynamic compressive strength of clay increased by 4 orders of magnitude compared to the static compressive strength. The dynamic strength of sorbothane increased by 3 orders of magnitude compared to the manufacturer specified static values. Only dynamic experiments, between strain rates of 2700 and 3700/sec, were performed on bologna. All the four materials showed very high strain-rate dependence. The tested materials showed similar stress-strain plots. Clay, Sorbothane and Bologna were very compliant up to 30 to 35% strains followed by a stiffer region where the stresses increased rapidly to the maximum values. The specimens were in stress equilibrium for significant time durations and specimen peak stresses where achieved during this period.     

Experimental investigation of high-strain rate properties of 3-D braided composite material in cryogenic field

This paper reports the high-strain rate properties of 3-D braided basalt/epoxy composite materials at 26 °C, −50 °C, −100 °C and −140 °C with strain-rate range from 1300 s⁻¹ to 2100 s⁻¹ by experimental study. A simple and effective cryogenic device was applied to the SHPB system to create the low-temperature field of the samples. It was found that the compression modulus, peak stress, failure strain and specific energy absorption of the 3-D braided basalt/epoxy composite materials had different sensitivity to temperatures and strain rates. In the out-of-plane impact, there were two failure modes, namely, compression-failure mode and shear-failure mode. Fracture of fiber tows was irregular with abundant pull-out of fiber and much finely-divided fragmentation of resin among fibers at room temperature. In cryogenic field, the fracture of fiber tows was neat and tidy with few pull-out of fiber and few finely-divided fragmentation of resin. However, in the in-plane impact, there was only compression failure mode. And there was no fracture of fiber tows and no big difference among samples tested under different gas pressures. Because of the function of squeezing and buckling, split-off separation of the composite could be blocked by the tangled fiber tows. As a whole, the reinforcement could still keep its structural integrity.     

Dynamic precipitation during cyclic deformation of an underaged Al-Cu alloy

The cyclic deformation behavior of Al-4Cu alloy containing shear-resistant particles was investigated systematically as a function of precipitate state. Pronounced cyclic hardening was observed in the under aged Al-4Cu-0.05Sn (wt.%) alloy strained under various imposed plastic strain amplitudes at room temperature. Such cyclic hardening is absent from the longer aging treatments. Microstructural characterization reveals that the pronounced cyclic hardening of the under aged alloy is due to the dynamic precipitation of GP zones. The dynamic precipitation occurs during all the cyclic loading process and only at the peak stress, where the hardening increment from dynamic precipitation saturates, does strain localization occur which is soon followed by failure of the material. The dynamic precipitation of GP zones has a positive effect on the low cycle fatigue performance of this alloy, and can significantly elevate the strength of this alloy without loss in ductility. Experiments performed to test the dependence of the cyclic hardening on plastic strain amplitude and strain-rate illustrate a relatively strain-rate independent and strain amplitude dependent behavior. Such kinetic behavior is approximately consistent with that expected if the GP zone formation is controlled by the vacancies production process during plastic deformation.     

Dynamic asymptotic mode III crack tip field in rate dependent materials

The asymptotic field at a dynamically growing crack tip in strain-rate sensitive elastic-plastic materials is investigated under anti-plane shear loading conditions. In the conventional viscoplasticity theory, the rate sensitivity is included only in the flow stress. However, it is often found that the yield strength is also affected by previous strain rates. The strain rate history effects in metallic solids are observed in strain rate change tests in which the flow stress decreases gradually after a rapid drop in strain rate. This material behavior may be explained by introducing the rate sensitivity in the hardening rule in addition to the flow rule. The strain-rate history effect is pronounced near the propagating crack where the change of strain rates take place. Effects of the rate dependency in the flow rule and the hardening rule on the crack propagation are analyzed. The order of the stress singularity in the asymptotic field is determined in terms of material parameters which characterize the rate sensitivity of the material. The results show that an elastic sector is present in the wake zone when the rate-dependency is considered only in the hardening rule. Terminal crack propagation speed is determined by applying the critical stress fracture criterion and the critical strain criterion to the asymptotic fields under the small scale yielding condition.     

聚脲材料动态压缩力学行为的数值模拟研究

以聚脲材料动态压缩力学特性为研究对象,提出了考虑动态弹性模量、动态强度因子和动态切线模量的简化三直线弹塑性本构模型;基于ANSYS/LS-DYNA有限元分析软件,建立了低、中、高不同应变率下聚脲材料压缩有限元模型,并与实验结果进行对比分析。结果表明：动态弹性模量增大因子、动态强度因子和动态切线模量因子随应变率增加而有规律的增大,均和应变率的对数呈双线性关系。在中低应变率下,三者的线性关系斜率都比较平缓;在高应变率下,三者的线性关系斜率都比较陡,且弹性模量动态增大因子的斜率比动态强度因子的更大,而第二阶段动态切线模量因子的斜率与动态强度因子的基本一致,但第三阶段动态切线模量因子的斜率是动态强度因子的2.3倍左右,说明高应变率下聚脲材料的后期应力强化效应更加显著。聚脲材料的简化三直线弹塑性本构模型可以在ANSYS/LS-DYNA有限元软件中较好地实现。该文建立的有限元模型能较为准确地模拟聚脲材料压缩实验,进一步验证了简化弹塑性本构模型在不同应变率压缩加载下的有效性。该研究可以为聚脲涂覆加固防护结构有限元模型提供材料模型参数依据。     

Modeling quasi-static and high strain rate deformation and failure behavior of a (±45) symmetric E-glass/polyester composite under compressive loading

Quasi-static (1 × 10⁻³–1 × 10⁻² s⁻¹) and high strain rate (∼1000 s⁻¹) compressive mechanical response and fracture/failure of a (±45) symmetric E-glass/polyester composite along three perpendicular directions were determined experimentally and numerically. A numerical model in LS-DYNA 971 using material model MAT_162 was developed to investigate the compression deformation and fracture of the composite at quasi-static and high strain rates. The compressive stress–strain behaviors of the composite along three directions were found strain rate sensitive. The modulus and maximum stress of the composite increased with increasing strain rate, while the strain rate sensitivity in in-plane direction was higher than that in through-thickness direction. The damage progression determined by high speed camera in the specimens well agreed with that of numerical model. The numerical model successfully predicted the damage initiation and progression as well as the failure modes of the composite.     

Estimation of biaxial tensile and compression behavior of polypropylene using molecular dynamics simulation

The polymeric materials in general exhibit strong time–temperature dependence and viscoelastic behavior. The time–temperature superposition principle is typically used to estimate the long-term viscoelastic behavior. In addition, Mises criterion and Tresca criterion have been proposed to estimate the yield or failure stresses in a multiaxial stress state and Christensen failure criterion can be applied in the case of different tensile and compressive strengths. In this study, using molecular dynamics method, uniaxial and biaxial tensile and compression test simulations were performed for polypropylene at various strain rates and temperatures. It was observed that the compressive fracture stresses were higher than the tensile fracture stresses. In addition, the fracture stress was high at a low temperature and high strain rate and these fracture stresses are in good agreement with Christensen failure criterion curves. Furthermore, the long-term viscoelastic behavior can almost be predicted from the short-term viscoelastic behaviors at three different temperatures using time–temperature superposition principle. But, the simulations at a wide range of temperatures is important to predict the more accurate long-term viscoelastic behavior.     

Stress/strain/time relations for ice under uniaxial compression

Results of mechanical tests involving uniaxial compression of isotropic ice at ?5°C were analysed and interpreted. Constant load (CL) creep tests were made for applied stresses in the range 0.8 to 3.8 MPa, and “strength” tests under constant displacement rate (CD) were made for applied strain rates in the range 10^?7 to 10^?3 s^?1. Results from CL tests and CD tests corresponded closely, giving much the same information about failure strains, strength, creep rates, time to failure, stress/strain-rate relations, and suchlike. Empirical stress/strain-rate relations were developed for three distinct states of strain: (1) for the initial yield point, where axial strains are typically of the order of 0.1%, (2) for the ductile yield point, where axial strains are typically of the order of 1%, (3) for an axial strain of 10%. Stress/strain-rate relations and stress/strain relations for constant duration of CL loading were examined for load durations up to half an hour. The elapsed time up to the ductile yield point (～1% strain) was related to stress and to strain rate for CL tests and CD tests, and correspondence of the results was demonstrated both for interrelationship between CL and CD tests and for compatibility with the appropriate stress/strain-rate relations. The elapsed time up to the initial yield point was also considered. It was shown that CD stress/strain curves can be constructed from a suitable family of CL creep curves, and vice versa.The characteristics of CL creep curves and CD stress/strain curves were examined in some detail, considering relations between strain rates for certain identifiable points on creep curves, and relations between stresses for certain identifiable parts of stress/strain curves. Effective values for quasi-elastic moduli were considered. The strains for various critical points were compared with each other and with the strains at which rates of acoustic emissions reach maximum values.     

Dynamic compressive behavior of unidirectional E-glass/vinylester composites

Results from an experimental investigation on the mechanical behavior of unidirectional fiber reinforced polymer composites (E-glass/vinylester) with 30%, 50% fiber volume fraction under dynamic uniaxial compression are presented. Specimens are loaded in the fiber direction using a servo-hydraulic material testing system for low strain rates and a Kolsky (split Hopkinson) pressure bar for high strain rates, up to 3000/s. The results indicate that the compressive strength of the composite increases with increasing strain rate. Post-test scanning electron microscopy is used to identify the failure modes. In uniaxial compression the specimens are split axially (followed by fiber kink band formation). Based on the experimental results and observations, an energy-based analytic model for studying axial splitting phenomenon in unidirectional fiber reinforced composites is extended to predict the compressive strength of these composites under dynamic uniaxial loading condition.     

Quasi-static and dynamic compression behaviour of an FPTM alumina-reinforced aluminium metal matrix composite

An aluminium metal matrix composite reinforced with continuous unidirectional -alumina fibres has been compression tested at quasi-static and dynamic strain rates. In the transverse direction, the composite showed increasing flow stress (at 5% strain) and maximum stress within the studied strain rates, 10^–3–3 × 10³ s^–1. In the longitudinal direction, the maximum stress of the composite increased similarly with increasing strain rates within the range 10^–5–7 × 10² s^–1. It is shown that, if brooming of the sample ends can be suppressed, the failure stress of the composite in longitudinal compression increases significantly. Metallographic observations reveal the typical modes of damage initiation in the composite.     

Cyclic loading and fatigue in ice

Isotropic polycrystalline ice was subjected to cyclic loading in uniaxial compression at ?5°C, with stress limits 0–2 and 0–3 MPa, and frequencies in the range 0.043 to 0.5 Hz. Stress-strain records showed hysteresis loops progressing along the strain axis at non-uniform rates. The effective secant modulus, which was about half the true Young's modulus, decreased during the course of a test. The elastic strain amplitude and the energy dissipated during a loading cycle both increased with increase of time and plastic strain. Strain-time records gave mean curves which were identical in form to classical constant-stress creep curves, with a small cyclic alternation of recoverable strain about the mean curve. The inflection point of the “creep curve”, marking the transition from strain hardening to strain softening, occurred at a plastic strain of 1% (±0.1%), which is about the same as the “ductile failure strain” found in constant stress creep tests and in constant strain-rate tests on ice of the same type at the same temperature. The dissipation of strain energy up to this “failure point” was much higher for the cyclic tests than for corresponding quasi-static tests ? 100 to 600 kPa (or kN-m/m³) in comparison to about 30 kPa. The number of cycles taken to reach the “failure point” was of no direct significance, varying greatly with stress amplitude and with frequency. The results of the tests suggest that maximum resistance under compressive cyclic loading occurs at an axial plastic strain of about 1%, which is essentially the same as the failure strain for ductile yielding under constant stress and under constant strain-rate.     

Viscoplastic response and modeling of asphalt-aggregate mixes

The strain response of asphalt-aggregate mixes to applied stresses is decomposed additively into a viscoelastic part and a viscoplastic part. The paper focuses on the response and modeling of the viscoplastic component; it includes the development of a multiaxial constitutive formulation that is capable of generating: (i) strain hardening when the loading is applied in one direction; (ii) strain softening immediately after stress reversals; (iii) volumetric changes under uniaxial conditions or isotropic conditions, or both; and (iv) directional non-symmetry. In order to investigate the model’s capabilities, four tests were performed sequentially on one asphalt sample. The tests were limited to pre-peak conditions and one temperature and consisted of creep and recovery sequences in uniaxial tension, uniaxial compression, isotropic compression and uniaxial tension-compression. Analysis of the results showed that the new theory, once calibrated, was able to adequately reproduce the viscoplastic strain component; its forecastability, however, was found limited.