Al2O3陶瓷材料应变率相关的动态本构关系研究

采用改进的SHPB实验方法对Al2O3陶瓷的动态力学性能进行了研究,得到了材料在较高应变率范围内的动态应力应变曲线。结果表明,Al2O3陶瓷为弹脆性材料,其动态应力应变呈非线性关系,在较高的应变率范围内,陶瓷材料的动态应力应变关系是应变率相关的;材料的初始弹性模量、破坏应力、破坏应变值随应变率的增大而增大。基于损伤力学的基本理论,给出了Al2O3陶瓷的一维损伤型线性弹脆性本构模型。根据SHPB实验结果确定模型中的参数,得到了Al2O3陶瓷应变率相关的损伤型动态本构方程。     

混凝土单轴受拉的非局部本构模型

混凝土受拉本构行为存在很强的局部软化现象,使得单轴受拉试验无法给出应力-应变关系,而只能给出应力-位移关系。本文根据内变量理论和等效应变假设建立了基于真实应变的混凝土单轴受力本构方程,并根据Weibull分布可以描述混凝土等脆性材料断裂过程的试验现象,建立了关于弹性应变的损伤演化规律。然后,通过假设平均应变与真实弹性应变的函数关系,在应力-平均应变的本构关系中采用平均弹性应变以描述其非局部行为,而在材料的损伤演化规律中采用真实弹性应变以描述其局部行为,由此建立了单轴受拉荷载条件下的非局部本构模型。最后,对一个单调受拉试验和一个反复受拉试验的仿真结果表明所提出的非局部本构模型可以准确地模拟试验结果。     

准脆性材料的弹塑性各向异性损伤耦合本构模型研究

针对准脆性材料的非线性特征：强度软化和刚度退化、单边效应、侧限强化和拉压软化、不可恢复变形、剪胀及非弹性体胀,在热动力学框架内,建立了准脆性材料的弹塑性与各向异性损伤耦合的本构关系。对准脆性材料的变形机理和损伤诱发的各向异性进行了诠释,并给出了损伤构形和有效构形中各物理量之间的关系。在有效应力空间内,建立了塑性屈服准则、拉压不同的塑性随动强化法则和各向同性强化法则。在损伤构形中,采用应变能释放率,建立了拉压损伤准则、拉压不同的损伤随动强化法则和各向同性强化法则。基于塑性屈服准则和损伤准则,构建了塑性势泛函和损伤势泛函,并由正交性法则,给出了塑性和损伤强化效应内变量的演化规律,同时,联立塑性屈服面和损伤加载面,给出了塑性流动和损伤演化内变量的演化法则。将损伤力学和塑性力学结合起来,建立了应变驱动的应力-应变增量本构关系,给出了本构数值积分的要点。以单轴加载-卸载往复试验识别和校准了本构材料常数,并对单轴单调试验、单轴加载-卸载往复试验、二轴受压、二轴拉压试验和三轴受压试验进行了预测,并与试验结果作了比较,结果表明,所建本构模型对准脆性材料的非线性材料性能有良好的预测能力。     

内爆炸载荷下圆管变形、损伤和破坏规律的研究

以物理统计和唯象研究相结合的方法,建立了微孔洞型的损伤函数模型和损伤演化方程,以变形热力学,Ｄｒｕｃｋｅｒ公设和内变量理论为基础建立了含损伤热塑性材料的增量型本构关系,用所建立的本构关系及损伤演化方程对内部爆轰作用下的圆管破坏过程完成了系列数值模拟,数值结果与实验结果相比较,在圆管变形过程,破坏时间,破坏速度,破坏应变,破坏应变率等信息方面都是基本一致的。     

碳纤维复合材料冲击模型率相关修正方法与试验研究

目前先进航空发动机的风扇叶片均采用复合材料结构,为了研究其在工作过程中可能受到的冲击损伤,即碳纤维增强树脂基复合材料受到高速冲击后的损伤与破坏过程,对其准静态下的正交各向异性本构模型和失效准则进行修正,建立了应变率相关的三维动态本构及损伤模型．该模型考虑了材料模量、强度和断裂韧性与应变率的相关性,并采用基于断裂韧性的渐进损伤模式对刚度进行折减来控制破坏过程．开展了不同应变率下的动态试验,得到基体方向拉伸与剪切的动态响应数据,拟合得到相应的动态修正因子．将该模型结合修正因子植入数值软件进行仿真计算,分析结果表明,所建立的率相关本构及损伤模型能够更准确地模拟层合板受冲击过程的损伤和破坏,与试验吻合较好．     

有机玻璃在高应变率下的损伤型非线性粘弹性本构关系及破坏准则

对两种有机玻璃高应变率下的大变形和破坏行为进行了实验研究,通过改进文献[2]本构关系的非线性弹性项并引入损伤参量,建立了一个适用于更大变形范围、能描述“应力平台”及“本构失稳”的损伤型非线性粘弹性本构方程。相应地,从临界损伤量概念出发,提出以应变和应变率为控制变量的破坏准则。不论是本构关系还是破坏准则,理论计算均与试验结果吻合良好。     

ABAQUS混凝土损伤塑性模型中损伤因子的率相关性及实现方法

ABAQUS程序中最常用的混凝土损伤塑性（concrete damage plasticity, CDP）模型无法实现损伤因子与应变率相关。为了准确描述混凝土材料在高应变率下的损伤特性,基于CDP模型定义了新的应变率场变量,编制了VUSDFLD用户子程序,开发了能够考虑损伤因子率相关性的改进的CDP（modified CDP,MCDP）模型。MCDP模型采用能量法求解混凝土拉压损伤因子,主求解程序能够随着应变率场变量的变化而自动更新不同应变率对应的损伤参数,计算得到的混凝土单轴静态加载结果与CDP模型吻合较好。MCDP模型对高应变率下动态压缩性能的模拟结果表明:混凝土材料在不同应变率下的拉压损伤对其动态力学性能有显著影响,编制的VUSDFLD子程序和MCDP模型能够有效地解决损伤应变率相关的模拟难题,可以准确地模拟爆炸荷载作用下钢筋混凝土梁的动态响应,为预测爆炸冲击等强动载作用下混凝土结构的响应和破坏提供了更可靠的技术途径。     

脆性固体非弹性和软化性能的损伤本构模拟

本文概要地介绍了作者近年来在脆性固体粘塑性损伤本构模型方面的工作。首先，通过假设损伤率依赖于粘塑性应变率和应力变化率，提出了一个考虑损伤演化及其对材料力学性能的影响的粘塑性损伤本构模型。     

含圆孔复合材料层板在拉伸载荷下损伤破坏过程的模拟

本文应用有限元法模拟受拉含孔夏合材料层板损伤起始、累积直至破坏的过程。在模拟中引入了作者早些时建立的包含基体开裂层非对称约束影响的损伤本构关系，以及裂纹密度与损伤区应力关系函数等。本文给出损伤累积模拟方法并编制了程序，用该程序可以获得层板加载过程中各层的损伤状态、计算其刚度衰减和应力重分布以及最终破坏载荷。给出了数值模拟算例并与现有研究结果进行了比较。     

水下爆炸对重力坝的毁伤效应及最优爆距

为研究不同爆距水下爆炸对重力坝的毁伤效应,并探讨是否存在“最优爆距”,基于离心模型试验建立了炸药-库水-空气-重力坝结构的全耦合数值模型,并设计了60组数值计算工况。不同工况水深均为600 mm,炸药量为2.2 g,重力坝模型几何比尺为1/80,包含5组爆深（50～250 mm）,每组爆深对应12组爆距,爆距范围为10～200 mm,相应比例爆距范围为0.077～1.54 m/kg1/3。对比分析了不同爆距水下爆炸对重力坝的毁伤程度,并定量比较了重力坝平均损伤、单元删除率、应力、应变等参数。结果表明,对于重力坝整体结构破坏,如重力坝整体弯曲导致的拉伸破坏,水下爆炸对重力坝的毁伤效应存在“最优爆距”,即随着爆距增加重力坝毁伤程度先增加后降低;与之类似,随着爆距的增加,重力坝上游坝面损伤区域的平均损伤、重力坝单元删除率、坝踵最大拉应力平均值和坝踵最大拉应变平均值先增加后降低且在40 mm爆距附近达到最大值。保持水深、炸药量和重力坝几何模型相同,5组不同爆深近水面水下爆炸对重力坝毁伤效应的“最优爆距”均在40 mm附近,表明近水面水下爆炸时爆深对“最优爆距”不存在显著影响。     

一个综合模糊裂纹和损伤的混凝土应变软化本构模型

本文研究就变软化材料的本构关系，提出了一个考虑损伤的粘塑性模型，损伤不仅影响材料的临界应力，而且影响材料的粘塑性，为模拟材料的应变软化行为，假设受损混凝土的破坏局部区域由模糊裂纹和损伤所统治，软化模量和局部区域尺度参量依赖于模糊裂纹扩展时释放的断裂能的参变量，用文中提出的模型计算了混凝土单轴压缩时不同应变速率下的瞬时应力应变响应以及等应力长期作用下的徐变，均得到很的结果。     

An interacting micro-crack damage model for failure of brittle materials under compression

A model is developed for brittle failure under compressive loading with an explicit accounting of micro-crack interactions. The model incorporates a pre-existing flaw distribution in the material. The macroscopic inelastic deformation is assumed to be due to the nucleation and growth of tensile “wing” micro-cracks associated with frictional sliding on these flaws. Interactions among the cracks are modeled by means of a crack-matrix-effective-medium approach in which each crack experiences a stress field different from that acting on isolated cracks. This yields an effective stress intensity factor at the crack tips which is utilized in the formulation of the crack growth dynamics. Load-induced damage in the material is defined in terms of a scalar crack density parameter, the evolution of which is a function of the existing flaw distribution and the crack growth dynamics. This methodology is applied for the case of uniaxial compression under constant strain rate loading. The model provides a natural prediction of a peak stress (defined as the compressive strength of the material) and also of a transition strain rate, beyond which the compressive strength increases dramatically with the imposed strain rate. The influences of the crack growth dynamics, the initial flaw distribution, and the imposed strain rate on the constitutive response and the damage evolution are studied. It is shown that different characteristics of the flaw distribution are dominant at different imposed strain rates: at low rates the spread of the distribution is critical, while at high strain rates the total flaw density is critical.     

应变损伤材料平面应力动态裂纹尖端场的渐近解

采用塑性动力学方程,对应变损伤材料的平面应力动态裂纹尖端场进行了渐近分析。假定损伤规律服从反比例关系,对平面应力问题,导出了本构方程,并给出了动态弹塑性场的渐近解,揭示了场的渐近特性。     

考虑混凝土应变率变化的高拱坝非线性动力响应研究

提出一种新的应变率相关的混凝土非线性弹塑性损伤模型。采用此模型对混凝土拱坝的非线性地震响应作了分析。在综合考虑坝-地基-库水动力相互作用和坝缝非线性接触的基础上，着重研究了混凝土应交率相关效应及加载历史对混凝土极限强度等重要参数及拱坝响应的影响，并与采用不考虑应交率影响的混凝土损伤模型计算结果进行了对比分析。结果表明，拱坝考虑横缝作用后的坝面应变率分布不同于整体拱坝。应交率分布形态不仅可以很好地表征拱坝的振动形态，而且对于高拱坝的动力响应的影响也不可忽略。     

综合考虑宏细观缺陷的岩体动态损伤本构模型

针对节理岩体同时含有节理、裂隙等宏观缺陷及微裂隙、微孔洞等细观缺陷的客观事实, 提出了在节理岩体动态损伤本构模型中应同时考虑宏细观缺陷的观点。为此, 首先对基于细观动态断裂机理的经典岩石动态损伤本构模型—TCK(Taylor-Chen-Kuszmaul)模型进行了阐述, 其次基于Lemaitre等效应变假设推导了综合考虑宏细观缺陷的复合损伤变量(张量), 进而在此基础上建立了相应的节理岩体动态损伤本构模型, 并利用该模型讨论了载荷应变率及节理条数对岩体动态力学特性的影响规律。结果表明, 在不同载荷应变率下试件在变形初始阶段是重合的, 而后随着应变的增加, 试件峰值强度、峰值应变及总应变均随载荷应变率的增加而增加; 随着节理条数的增加, 试件峰值强度逐渐降低, 但降低趋势逐渐变缓并趋于某一定值。上述研究结论与目前的理论及实验研究结果的基本规律是一致的, 说明了本模型的合理性。     

A rate-dependent damage model for brittle materials based on the dominant crack

A rate-dependent, continuum damage model is developed for brittle materials under dynamic loading. This model improves on the approach (ISOSCM) of [Addessio, F.L., Johnson, J.N., 1990. A constitutive model for the dynamic response of brittle materials. Journal of Applied Physics 67, 3275–3286] in several respects. (1) A new damage surface is found by applying the generalized Griffith instability criterion to the dominant crack (having the most unstable orientation), rather than by averaging the instability condition over all crack orientations as done previously. The new surface removes a discontinuity in the damage surface in ISOSCM when the pressure changes sign. (2) The strain due to crack opening is more consistent with crack mechanics, with only the tensile principal stresses contributing to the crack opening strain. This is achieved by incorporating a projection operator in the equation for the crack opening strain. One consequence of incorporating the projection operator is a prediction of shear dilatancy, which is not accounted for in ISOSCM. (3) The evolution of damage, which is based on the energy-release rate for the dominant crack, has a physical basis, whereas in the previous approach the damage growth rate was assumed to be an exponential function of the distance from the stress state to the damage surface without specific physical justification.An implicit algorithm has been developed so that a larger time step can be used than with the explicit algorithm used in ISOSCM. The numerical results of a silicon carbide (SiC) ceramic under several loading paths (hydrostatic tension/compression, uniaxial strain, uniaxial stress, and shear) and strain rates are presented to illustrate the main features of the model.     

6061-T6铝合金动态拉伸本构关系及失效行为

采用HMH-206高速材料试验机开展了6061-T6铝合金在0.001～100 s?1应变率范围内的静、动态拉伸力学性能实验,分析了其应力-应变响应特征和应变率敏感性,讨论了应变率对6061-T6铝合金流动应力和应变率敏感性指数的影响,并基于实验结果对Johnson-Cook本构模型进行了修正。结合缺口试件的实验结果和模拟数据,得到了材料的Johnson-Cook失效模型参数,并对模型的准确性和适用性进行了验证。结果表明,在拉伸载荷作用下,6061-T6铝合金表现出明显的应变硬化特征和应变率敏感性,其流动应力随应变率的升高而提高,修正的Johnson-Cook本构模型可以描述材料的动态塑性流动行为,建立的Johnson-Cook失效模型能够表征材料的断裂失效行为。     

Constitutive relationship of brittle rock subjected to dynamic uniaxial tensile loads with microcrack interaction effects

A micromechanical model is proposed to describe both stable and unstable damage evolution in microcrack-weakened brittle rock material subjected to dynamic uniaxial tensile loads. The basic idea of the present model is to classify the constitution relationship of rock material subjected to dynamic uniaxial tensile loads into four stages including some of the stages of linear elasticity, pre-peak nonlinear hardening, rapid stress drop, and strain softening, and to investigate their corresponding micromechanical damage mechanisms individually. Special attention is paid to the transition from structure rearrangements on microscale to the macroscopic inelastic strain, to the transition from distribution damage to localization of damage and the transition from homogeneous deformation to localization of deformation. The influence of all microcracks with different sizes and orientations are introduced into the constitutive relation by using the statistical average method. Effects of microcrack interaction on the complete stress-strain relation as well as the localization of damage for microcrack-weakened brittle rock material are analyzed by using effective medium method. Each microcrack is assumed to be embedded in an approximate effective medium that is weakened by uniformly distributed microcracks of the statistically-averaged length depending on the actual damage state. The elastic moduli of the approximate effective medium can be determined by using the dilute distribution method. Micromechanical kinetic equations for stable and unstable growth characterizing the ‘process domains’ of active microcracks are taken into account. These ‘process domains’ together with ‘open microcrack domains’ completely determine the integration domains of ensemble averaged constitutive equations relating macro-strain and macro-stress. Theoretical predictions have shown to consistent with the experimental results.     

A fracture damage model for Jointed rock masses and its application to the stability analysis of dam abutments

Based on continuum damage mechanics, for jointed rock masses, a fracture damage model is presented in this paper. First, the damage tensors are defined through the elastic-flexibility of intact rock and the equivalent elastic-damage flexibility for rock mass. Then, by the self-consistent principle of solid mechanics, the equivalent elastic-damage flexibility tensors involving the interaction between multicracks are deduced. The damage evolution law is proposed involving the mechanism of crack propagation process: frictional sliding, crack kinking, growing of branched tension cracks, interlinking of the microcracks near branched crack tips leading to the breakthrough of macro-cracks and finally the failure of rock mass. Thus the evolution of damage variables reasonably unified with the process of crack propagation is given. Finally, a plastic-brittle damage constitutive relation including brittle coupled strain rate, developed and applied to the stability analysis of complicated rock foundation of a dam in China, is described in this paper.