Sufficient criterion of fracture in the case with a complex stress state and non-proportional deformation of the material in the pre-fracture zone

A general case of proportional loading with a complex stress state of the material in the pre-fracture zone, which is typical for polycrystalline solids with plastic deformation, is considered. A sufficient criterion of fracture is proposed for the case of a complex stress state with non-proportional deformation of the material in the pre-fracture zone. Critical parameters of fracture (pre-fracture zone length and load) for cracks propagating in quasi-brittle materials are obtained with the use of a modified Leonov-Panasyuk-Dugdale model. The pre-fracture zone width is determined by solving the problem of the plasticity theory in the vicinity of the crack tip. The proposed modification of the Leonov-Panasyuk-Dugdale model makes it possible to estimate the critical opening of the crack and the critical displacement of the crack flanks. Inequalities that describe different mechanisms of material fracture under proportional loading (predominantly shear fracture mechanism and fracture mechanism through cleavage) are derived.     

爆炸载荷特征参数对无限长圆柱壳弹性动态响应的影响

采用含有三角脉冲载荷和准静压载荷的爆炸载荷加载,利用单自由度模型对无限长圆柱壳体（即等效平面应变圆环）的弹性动态响应进行了力学分析,获得了径向位移响应解析解及准静压阶段弹性响应振幅的解析解。基于所得解析解,通过控制变量法分析了载荷压力及载荷分界点时刻（即三角脉冲载荷与准静压载荷作用的分界点时刻）对径向位移最大值、准静压阶段弹性响应振幅的影响规律,更加深入地研究了爆炸载荷对结构响应的影响。本文主要从准静压幅值与三角脉冲峰值的比值以及载荷分界点时刻两个主要特征参数入手,结合结构的呼吸振动频率来研究爆炸载荷对无限长圆柱壳弹性动态响应的影响。在研究中发现存在临界时刻:当载荷分界点时刻早于临界时刻时,径向位移最大值出现在准静压阶段;当载荷分界点时刻晚于临界时刻时,获得了便于直观判断径向位移达到最大值时所处载荷阶段的分区图。基于前述解析解的分析,还获得了不同影响因素导致的振幅变化的单调性分区图,便于判别载荷压力的变化所致的准静压阶段振幅的增减趋势。通过研究获得的爆炸压力载荷对结构响应的影响规律,可为爆炸容器设计以及结构防护基础研究提供参考。     

纤维复合材料界面横向拉伸分析

以单纤维十字型横向拉伸试验为研究对象,对纤维/基体界面采用弹性-软化双线性内聚力模型,建立了纤维复合材料在横向拉伸作用下界面法向失效过程的解析模型。得到了沿纤维/基体圆周界面的法向应力分布,纤维/基体界面的状态与界面承载力和单纤维复合材料承载力的关系,以及内聚力参数和试件几何尺寸对它们的影响。结果表明:纤维/基体圆周界面在脱粘前经历全部弹性及弹性+软化两种状态;当界面为弹性状态时,界面法向应力随界面强度线性增加;当界面为弹性+软化状态时,界面软化范围随界面裂纹萌生位移的增加而增大;界面初始脱粘位置与拉伸荷载方向重合;界面初始脱粘时的界面承载力随界面强度及界面裂纹萌生位移的增加而增加,随界面裂纹生成位移的增加而降低;单纤维复合材料的脱粘荷载受基体截面尺寸的影响,当纤维体积含量相同时,沿荷载方向截面尺寸的增大对提高脱粘荷载更显著。     

Damage model and damage assessment for single-layer reticulated domes under exterior blast load

Long-span reticulated dome is often considered as a landmark building of a region, so it is very important to investigate the dynamic response and propose the damage assessment method of reticulated dome under blast loading. In this article, a fine finite element model of Kiewitt8 (K8) single-layer reticulated dome was established by using ANSYS/LS-DYNA. The effects of standoff distance, charge weight, rise–span ratio, span, and roof weight on the responses of K8 single-layer reticulated dome were numerically studied. The results showed that the blast-resistant performance of reticulated dome with smaller rise–span ratio and larger span under exterior blast load was more advantageous. Although the blast-resistant capacity of reticulated dome with large span and large roof weight was favorable, the plastic deformations of reticulated dome members were small and the utilization of material was low at failure state. According to the dynamic response characteristics of plentiful K8 single-layer reticulated domes at different damage levels, a damage model of K8 single-layer reticulated dome under exterior blast load was proposed in this article to indicate the damage level and determine the ultimate strength. Besides, a new damage criterion for K8 reticulated dome was also defined. This damage model was defined based on the physical phenomena at different damage levels, which made the strength failure criterion had definite physical meaning. Using the proposed damage criterion and a new search algorithm for pressure and impulse, the pressure–impulse diagrams for the typical K8 reticulated dome were derived from the numerical simulations to evaluate the damage level of reticulated dome under blast loading. Finally, a method to determine the safety standoff distance for reticulated dome under given TNT charge weight was also proposed.     

Application of a stress triaxiality dependent fracture criterion in the finite element analysis of unnotched Charpy specimens

Nonlinear dynamic finite element analysis (FEA) is conducted to simulate the fracture of unnotched Charpy specimens of steel under pendulum impact loading by a dedicated, oversized and nonstandard Bulk Fracture Charpy Machine (BFCM). The impact energy needed to fracture an unnotched Charpy specimen in a BFCM test can be two orders of magnitude higher than the typical impact energy of a Charpy V-notch specimen. To predict material failure, a phenomenological, stress triaxiality dependent fracture initiation criterion and a fracture evolution law in the form of strain softening are incorporated in the constitutive relations. The BFCM impact energy results obtained from the FEA simulations compare favorably with the corresponding experimental data. In particular, the FEA predicts accurately the correlations of the BFCM impact energy with such factors as specimen geometry, impactor tup width and material type. The analyses show that a specimen’s progressive deterioration through the thickness dimension displays a range of shear to ductile fracture modes, demonstrating the necessity of applying a stress state dependent fracture initiation criterion. Modeling the strain softening behavior helps to capture the residual load carrying capability of a ductile metal or alloy beyond the onset of damage. The total impact energy can be significantly under predicted if a softening branch is not included in the stress-strain curve. This research supports a study of the puncture failure of railroad tank cars under dynamic impact loading. Applications of the presented fracture model in failure analyses of other structures are further discussed.     

Electromechanical impact of a crack in a functionally graded piezoelectric medium

The Mode-I transient response of a functionally graded piezoelectric medium is solved for a through crack under the in-plane mechanical and electric impact. Integral transforms and dislocation density functions are employed to reduce the problem to singular integral equations. Numerical results display the effects of the loading combination parameter λ and the material parameter βa on the dynamic stress intensity factor and electric displacement intensity factor. The energy density factor criterion is applied to obtain the maximum of the minimum energy density factor and the direction of crack initiation.     

Energy principle of ferroelectric ceramics and single domain mechanical model

Many physical experiments have shown that the domain switching in a ferroelectric material is a complicated evolution process of the domain wall with the variation of stress and electric field. According to this mechanism, the volume fraction of the domain switching is introduced in the constitutive law of ferroelectric ceramic and used to study the nonlinear constitutive behavior of ferroelectric body in this paper. The principle of stationary total energy is put forward in which the basic unknown quantities are the displacement u _i , electric displacement D _i and volume fraction ρ _I of the domain switching for the variant I. Mechanical field equation and a new domain switching criterion are obtained from the principle of stationary total energy. The domain switching criterion proposed in this paper is an expansion and development of the energy criterion. On the basis of the domain switching criterion, a set of linear algebraic equations for the volume fraction ρ _I of domain switching is obtained, in which the coefficients of the linear algebraic equations only contain the unknown strain and electric fields. Then a single domain mechanical model is proposed in this paper. The poled ferroelectric specimen is considered as a transversely isotropic single domain. By using the partial experimental results, the hardening relation between the driving force of domain switching and the volume fraction of domain switching can be calibrated. Then the electromechanical response can be calculated on the basis of the calibrated hardening relation. The results involve the electric butterfly shaped curves of axial strain versus axial electric field, the hysteresis loops of electric displacement versus electric filed and the evolution process of the domain switching in the ferroelectric specimens under uniaxial coupled stress and electric field loading. The present theoretic prediction agrees reasonably with the experimental results given by Lynch. The project supported by the National Natural Science Foundation of China (10572138).     

Plasticity aspects of interfacial fracture for polymer/glass specimens

Experimental results suggest that the interfacial fracture resistance is minimal for approximate near tip Mode I accompanied by positive and negative near tip Mode II. Finite-strain FE analysis is made for an elastic–plastic medium bonded to an ideally elastic medium with an interface crack. Small-scale plasticity conditions are invoked and examined in relation to the elastic–plastic stress distribution along the bond line. Plasticity engenders a tendency to turn near tip biaxiality towards pure Mode I regardless of the mixed-mode loading. High levels of hydrostatic stress are attained. For different mode mixities of the applied load, the dependence of the elastic–plastic normal bond stress on load level is examined. It is found that under positive Mode II loading, the normal bond stress σ_yy tends to saturate as the load level rises. This does not occur for Mode I and negative Mode II loading. In addition, deformation patterns inside the plastic zone are examined for mixed-mode situations. A displacement criterion based on the normal bond crack opening suggests a dependence of the critical load level on the extent of mixed mode. Under positive mode II fracture, traces of the ductile material are found at the top of the elastic substrate. Some of these conclusions appear to be consistent with the fracture patterns observed for LD-polyethylene/glass interfacial mixed-mode fracture.     

Modelling of crack growth by fracture damage zone

The strain energy density (SED) criterion is applied for analyzing the full range of mixed mode fracture from tensile to shear loading. A fracture damage zone (FDZ) local to the crack tip is defined and discussed in connection with the influence of crack geometry, loading and local material property. The size of FDZ tends to change continuously from statically to cyclically applied load conditions. It can be estimated from the uniaxial mechanical properties of the material. Both experimental and analytical results are examined for subcritical crack growth under static loading that depends on the type steel structures the fracture behavior of which could be represented by a single curve for the given specimen geometry.     

Crystallographic failure analysis of film near cooling hole under temperature gradient of nickel-based single crystal superalloys

In this paper, a unit cell model with a film cooling hole has been set up to analyze the crystallographic stress characterization and failure behavior under temperature gradient of nickel-base single crystallographic superalloys (SC). The aim of this work is to study the failure behavior of SC blades with film cooling. The distribution of cooling air pressure on the hole side surface and the distribution of the temperature around the hole are obtained from the fluid analysis. The result of the temperature distribution is then transferred to the finite element model (cell model) by the interpolation method. The cell model is analyzed by the crystallographic rate dependent finite element method (FEM). Special attention is put on the influence of temperature gradient. The influence of the loading boundaries, i.e. displacement loading and stress loading, on the stress characterization around hole is also taken into consideration. The results show that temperature gradient hole has much influence on the stress characterization. Different types of loading boundaries result in different types of stress and strain distributions. There is clear stress concentration near the hole under displacement loading, while there is clear strain concentration under stress loading. The failure characterization has been studied by the strain energy density criterion. It is shown that the temperature gradient has influence on the failure behavior.     

Response and Damage Tolerance of Composite Sandwich Structures under Low Velocity Impact

The deformation and failure response of composite sandwich beams and panels under low velocity impact was reviewed and discussed. Sandwich facesheet materials discussed are unidirectional and woven carbon/epoxy, and woven glass/vinylester composite laminates; sandwich core materials investigated include four types of closed cell PVC foams of various densities, and balsa wood. Sandwich beams were tested in an instrumented drop tower system under various energy levels, where load and strain histories and failure modes were recorded for the various types of beams. Peak loads predicted by spring-mass and energy balance models were in satisfactory agreement with experimental measurements. Failure patterns depend strongly on the impact energy levels and core properties. Failure modes observed include core indentation/cracking, facesheet buckling, delamination within the facesheet, and debonding between the facesheet and core. In the case of sandwich panels, it was shown that static and impact loads of the same magnitude produce very similar far-field deformations. The induced damage is localized and is lower for impact loading than for an equivalent static loading. The load history, predicted by a model based on the sinusoidal shape of the impact load pulse, was in agreement with experimental results. A finite element model was implemented to capture the full response of the panel indentation. The investigation of post impact behavior of sandwich structures shows that, although impact damage may not be readily visible, its effects on the residual mechanical properties of the structure can be quite detrimental.     

Failure behavior of composite sandwich structures under local loading

Usually when analyzing the mechanical response of foam-cored fiber-reinforced composite sandwich structures to localized static loading, the face sheets are treated as a linear-elastic material and no damage initiation and growth is considered. However, practice shows that at higher indentation magnitudes damage develops in the face sheet in the area of contact with the indentor, which could lead to local failure of the face laminate due to the loss of bending stiffness and strength. Therefore, the main objective of the present study is to develop a damage model for predicting the local failure in the composite face sheet and its influence on the load–displacement behavior of sandwich structures under local loading. For this purpose, the Hoffman failure criterion is incorporated into a finite element modeling procedure using the ABAQUS program system. Results deducted from the modeling procedure are compared with experimental data obtained in the case of static indentation tests performed on sandwich beam specimens using steel cylindrical indentors. It is shown that taking into account the damage in the face sheet leads to a substantial improvement in the performance of the model when simulating the mechanical behavior of the sandwich structures at higher indentation values.     

Nonlinear dynamic buckling of a viscoelastic model under impact loading

A simple nonlinear buckling analysis is applied to a one-degree-of-freedom arch under impact loading in which viscous damping may also be included. Such a loading consists of a falling body striking centrally the joint mass of the arch in such a way that a completely plastic impact can be postulated. When there is no damping the exact dynamic buckling load for such a kind of loading-associated with an unbounded motion can be established by using a static criterion (approach). More specifically, it was shown that the dynamic buckling load corresponds to that unstable equilibrium state where the total potential energy of the system is zero. Furthermore, it was proved that the second variation of the total potential energy at the foregoing unstable equilibrium state is negative definite. This implies that the curve loading versus displacement resulting by the vanishing of the total potential energy has always a maximum on the afore mentioned unstable state. It was also found that the system may become sensitive to initial conditions. If damping is included the foregoing static criterion yields lower bound buckling estimates. These findings were verified by employing a highly efficient approximate technique as well as the numerical scheme of Runge-Kutta for solving any nonlinear initial-value problem.     

Full-Field Deformation Measurements of Aluminum Plates Under Free Air Blast Loading

Assessment of the structural dynamic response caused by an explosion is complex due to the high velocity impact, the transient nature of the deformation and the interactions between the structure and the pressure wave. This paper deals with full-field measurements of aluminum plates under free air blast loading conditions. Forty grams of explosive material C4 is detonated at a stand-off-distance of 250?mm and two synchronized high-speed cameras in a stereoscopic setup are used to capture the plate response with an inter frame rate of 6,000 fps. The transient deformation fields are calculated using a three-dimensional digital image correlation technique. The observations appeared to be interesting and somewhat counter intuitively. Results show that a free air blast load induces a highly localized, rapid material response which can be essentially divided in two different stadia. First, when the shock impulse occurs, all particles are forced to move out-of-plane and provided with initial velocities. Secondly, when the pressure wave has vanished, the deformation is further driven by this imparted momentum. This paper shows that a 3D high-speed DIC system is a powerful tool for the assessment of the dynamic response of a structure subjected to extreme loading conditions such as explosions and that this system is capable of accurately measuring surface displacement and deformation data at high rates. Moreover, a free air blast load makes it possible to load a plate specimen at different strain rates in different zones. This makes the test suitable for future material identification using inverse methods, which profit from heterogeneous displacement and strain fields.     

考虑平稳随机响应的显式结构拓扑优化

随机载荷是工程结构在服役中经常承受的一种复杂的载荷形式,通常采用统计学特性对其进行描述。对随机载荷作用下的结构进行拓扑优化设计是一项极具挑战性的工作,其主要难点在于,(1) 传统隐式拓扑优化方法的设计变量数巨大,且用于结构动态性能拓扑优化问题时存在虚假模态等数值不稳定问题; (2) 对结构的随机动力响应统计量及其灵敏度进行计算需要极大的计算量; (3) 隐式拓扑优化框架下的分析模型与优化模型强耦合,导致结构有限元模型具有极高的自由度,进一步加剧了上述困难。本文基于移动可变形组件框架和虚拟激励法理论,提出了一种平稳随机载荷作用下结构的显式拓扑优化设计方法。通过将一系列可移动和可变形的结构组件作为优化的基础单元,实现了使用少量设计变量描述结构拓扑构型的目的。采用虚拟激励法、自由度删除技术和模态位移法有效降低了对结构进行随机振动分析和灵敏度分析的计算量。在此基础上,以结构柔顺度的标准差为目标函数、以设计域内实体材料的体积为约束条件,实现了限带白噪声作用下结构的拓扑优化设计,并通过数值算例验证了本文方法的有效性。     

Crack initiation behavior of functionally graded piezoelectric material: prediction by the strain energy density criterion

Transient response of a functionally graded piezoelectric medium is considered for a through crack under the mixed-mode in-plane mechanical and electric load. Integral transforms and dislocation density functions are employed to reduce the problem to singular integral equations. The energy density factor criterion is applied to obtain the maximum of the minimum energy density factor. This determines the direction of crack initiation. Numerical results display the effects of material constants, loading combination parameter, mechanical loading angle and material gradient parameter on the possible fracture behavior.     

Scaling of size/time/temperature — Part 2: Progressive damage in uniaxial compressive specimen

This work is concerned with predicting the fatigue failure initiation of a wing/fuselage bolt assembly. Accounted for in the analysis are both the influence of energy dissipation and damage accumulation as the structure is subjected to repeated cyclic loading. Results involving the location and number of cycles to initiate a fatigue crack 10⁻² in. are obtained. They agreed both qualitatively and quantitatively with the experimental findings. Also discussed is the influence of pre-torque in the bolt which tends to decrease the number of cycles to fatique crack initiation. Fatigue life may be extended by altering the load path so as to decrease the accumulation of energy near the site of failure initiation. This can be accomplished without major modification of the design. The methodology that makes use of the strain energy density criterion can be used to optimize the fatigue strength of other structural sub-assemblies by appropriate combination of material and geometry for specified load conditions.     

Mesoscale fatigue failure of welded joints of low-alloy steel

The fatigue failure kinetics for welded joints of low-alloyed steel is investigated by analyzing the displacement vector field under high-cyclic loading. Failure accumulation in the heat-affected zone at the mesoscale is found to possess a multi-stage character that is associated with the formation and evolution of mesostructure deformation and fragmentation. Identified are the pertinent parameters that described the mechanical state of welded joints under load.     

轴向冲击下C型冷弯卷边槽钢构件的动力响应

针对轴向冲击载荷下C型冷弯薄壁钢构件的动力响应,采用商业有限元软件Abaqus建立了能够反映冲击过程的有限元模型。通过对比有限元模拟和落锤实验中利用数字散斑技术采集的数据以及试样残余变形,验证了数值模型的可靠性。采用该模型分析了在不同冲击速度下翼缘、腹板和卷边质点的轴向位移-时间曲线以及腹板横向挠度的变化,结果表明:在较低冲击能量的作用下,翼缘对卷边的约束作用明显;而在较高冲击能量的加载过程中,冲击端卷边的轴向位移和速度明显大于翼缘和腹板,卷边破坏严重;随着冲击速度的提升,C型冷弯薄壁钢构件的动态屈曲临界载荷相应提升。