Imperfection and burial-depth sensitivity of the initiation and development of kink folds in laminated rocks

The first objective is to study the influence of the burial depth and of an imperfection, in the form of a tilt in the inclination of the otherwise straight, laminated beam, on the conditions for the initiation and the development of kink folds. The beam, typical of sedimentary rocks, is layered with weak interfaces between the competent beds, promoting the onset of kinking by their slip. The results are analytical and based on the upper bound approach of the classical limit analysis, referred to as the maximum strength theorem in the absence of any discussion of plasticity. The weak interface strength is described by the Coulomb criterion, whereas the bulk material is also cohesive and frictional but with an additional closure in the compressive stress domain to depict the action of compacting deformation mechanisms. The new twist to the methodology is to extend its application to the development of the failure mode beyond the onset, assuming that the structure finite response is well described by the least upper bound solution. The second objective is to compare in terms of upper bounds three different failure mechanisms which are the compaction band, the reverse fault and the kink fold. Their respective domain of dominance is constructed in failure-mechanism maps in the space spanned by the imperfection angle and the burial depth.Compaction bands are predicted at the deepest end of the beam and the reverse fault and the kink fold at the shallower end. These depth differences are resulting from the geometrical imperfection. It is found that the kink-band mode at its onset, with compaction band dominant conditions, resembles to a slip-enhanced compaction band due to the weak interface activation and the compaction along the two parallel hinges. This hybrid mode migrates suddenly through the competent beam from the deepest towards the shallowest region and develops as a kink fold, after a negligible amount of shortening. The kink fold development, beyond the onset, occurs in two phases, the first corresponding to the rotation of the kink band and the second, to its widening. The associated least upper bound is first decreasing during the development and then increasing, the minimum being controlled more by the increase in the potential energy of the system than by the most favorable orientation of the frictional weak interfaces. It is finally found that the continuous activation of slip over the weak interfaces and the widening of the kink band prevent the rotation of the kink towards the large angles which are necessary to induce its locking. It is proposed that the introduction of damage along the hinges could palliate these two effects and prompt the locking observed experimentally and in the field.     

SHPB冲击作用下层状千枚岩多尺度破坏机理研究

通过分离式霍普金森杆对层状千枚岩施加动态载荷,得到不同层理倾角下层状千枚岩的动态抗压强度与宏观破坏模式。采用三维激光仪获得断裂面细观形貌,引入分形几何定量计算断口面粗糙度;结合SEM观察到的微观尺度下不同层理倾角断口破坏机理,分析了不同层理倾角下层状岩石的动态破坏机制。研究结果表明:动态压缩下层理弱面对岩石的抗压强度影响较大;不同层理倾角千枚岩的断口形貌分形维数随层理倾角增大呈U型变化;从强度与裂纹扩展两方面考虑层理弱面对层状岩石破坏特征的影响,对于层理倾角为0°的试样,强度由岩石基质控制,但层理弱面仍对岩石破坏的裂纹分布与走向产生较大影响;对于层理倾角为22.5°的试样,强度与裂纹走向受岩石基质与层理弱面共同控制;对于层理倾角为45°~67.5°的试样,强度与裂纹走向受层理弱面控制;而对于层理倾角为90°的试样,动态抗压强度受岩石基质的影响较大,在层理弱面较早形成纵向宏观裂纹,导致该层理弱面角度下裂纹受层理弱面的影响较大。     

On the axial propagation of kink bands in fiber composites : Part i experiments

In many fiber composites, longitudinal compressive failure leads to the formation of kink bands. It has been found that these kink bands, once formed, can be made to propagate (broaden) in a steady-state manner at a constant stress level called the propagation stress (σ_P) . This is a characteristic stress of the material which, for the AS4⧹PEEK composite used in the study reported here, is approximately 40% of its compressive strength. This phenomenon is investigated experimentally using a special confining set-up that allows direct observation of the propagation process. For the composite studied, the kink bands have a repeatable inclination (β) of approximately 15°, and the fibers within the bands are rotated to about 30° in the absence of a load. When loaded to σ_P, however, they are found to rotate further to 40°, that is, substantially greater than the 2β reported elsewhere. The mechanism of propagation is found to be a bend-break-rotate sequence undergone by short segments of fibers at the edge of the kink band. It is well known that polymeric matrix composites such as the one used in this study exhibit rate-dependent behavior. Experimental results are presented which show that the kink band propagation stress is also rate dependent.     

Novel stacked folded cores for blast-resistant sandwich beams

Recent research has established the effectiveness of sandwich structures with metallic cellular cores for blast mitigation. The choice of core architecture can enhance sandwich performance, dissipating energy through plastic core compression and exploiting fluid–structure interaction effects to reduce the momentum imparted to the structure by the blast. In this paper we describe the first analysis of a novel sandwich core concept for blast mitigation: the stacked folded core. The core consists of an alternating stacked sequence of folded sheets in the Miura (double-corrugated) pattern, with the stack oriented such that the folding kinematics define the out-of plane compressive strength of the core. It offers a number of distinct characteristics compared to existing cellular cores. (i) The kinematics of collapse of the core by a distinctive folding mechanism give it unique mechanical properties, including strong anisotropy. (ii) The fold pattern and stacking arrangement is extremely versatile, offering exceptional freedom to tailor the mechanical properties of the core. This includes freedom to grade the core properties through progressive changes in the fold pattern. (iii) Continuous manufacturing processes have been established for the Miura folded sheets which make up the core. The design is therefore potentially more straightforward and economical to manufacture than other metallic cellular materials. In this first investigation of the stacked folded core, finite element analysis is used to investigate its characteristics under both quasi-static and dynamic loading. A dynamic analysis of an impulsively loaded sandwich beam with a stacked folded core reveals the versatility of the concept for blast mitigation. By altering the fold pattern alone, the durations of key phases of the dynamic sandwich response (core compression, beam bending) can be controlled. By altering both fold pattern and sheet thickness in the core, the same is achieved without altering the density of the core or the mass distribution of the sandwich beam.     

The microbuckling failure of Dyneema~? composites under compression

Two grades of Dyneema~?composite laminates with the commercial designations of HB26 and HB50 were cut into blocks with or without an edge crack and compressed in the longitudinal fiber direction. The cracked and uncracked specimens show similar compressive responses including failure pattern and failure load. The two grades of Dyneema~? composites exhibits different failure modes: a diffuse, sinusoidal buckling pattern for Dyneema~? HB50 due to its weak matrix constituent and a kink band for Dyneema~? HB26 due to its relatively stronger matrix constituent. An effective finite element model is used to simulate the collapse of Dyneema~? composites, and the sensitivity of laminate compressive responses to the overall effective shear modulus, interlaminar shear strength, thickness and imperfection angle are investigated. The change of failure mode from kink band to sinusoidal buckling pattern by decreasing the interlaminar shear strength is validated by the finite element analyses.     

Kink band propagation in layered structures

Confined layered structures in layer-parallel compression exhibit kink band deformation that has an associated severe initial instability. However, once the first kink band forms the system restabilizes and the bands then propagate in two mechanisms: band broadening and band progression. Previous work on triggering the initial instability and band broadening is now extended to include band progression. A new model for this propagation mechanism that successfully accounts for the modulating restabilizing response is presented and quantitative comparisons with the physical experiments yield excellent results.     

Design and analysis of a novel 6-DOF redundant actuated parallel robot with compliant hinges for high precision positioning

This paper presents the design and modeling of a new 6-DOF 8-PSS/SPS compliant dual redundant parallel robot with wide-range flexure hinges. This robot can achieve either high accurate positioning or rough positioning as well as a 6-DOF active vibration isolation and excitation to the payload placed on the moving platform. Adopting a kind of wide-range flexure hinge, we establish the kinematics model of the macro parallel mechanism system via the stiffness model and Newton–Raphson method, then we build up the dynamics model using Kane’s method for the micro-motion system. The investigations of this paper will provide suggestions to improve the structure and control algorithm optimization for a novel compliant dual redundant parallel mechanism in order to achieve the feature of larger workspace, higher motion precision and better dynamic characteristics. The results will be helpful in modifying the structure of the prototype platform to enhance its high kinematics and dynamics properties.     

Compressive failure of fiber composites under multi-axial loading

This paper examines the compressive strength of a fiber reinforced lamina under multi-axial stress states. An equilibrium analysis is carried out in which a kinked band of rotated fibers, described by two angles, is sandwiched between two regions in which the fibers are nominally straight. Proportional multi-axial stress states are examined. The analysis includes the possibility of bifurcation from the current equilibrium state. The compressive strength of the lamina is contingent upon either attaining a load maximum in the equilibrium response or satisfaction of a bifurcation condition, whichever occurs first. The results show that for uniaxial loading a non-zero kink band angle β produces the minimum limit load. For multi-axial loading, different proportional loading paths show regimes of bifurcation dominated and limit load dominated behavior. The present results are able to capture the beneficial effect of transverse compression in raising the composite compressive strength as observed in experiments.     

重庆市涪陵区厚层软硬相间岩体失稳模式

重庆市涪陵区厚层软硬相间公路高边坡的详细调查发现,不同的岩层产状,不同开挖方向其斜坡变形破坏模式不同。本文根据野外实例总结了不同岩层产状与开挖方向对应的破坏模式,平缓层状斜坡破坏方式有滑塌式崩塌、倾倒式崩塌和坠落式崩塌;中倾角层状斜坡破坏方式有顺层滑移和崩塌;高陡倾角层状斜坡坡破坏方式有滑移式崩塌和坠落式崩塌。表明斜坡变形破坏地质力学模式与斜坡岩体结构之间存在着密切的成生联系。通过对不同倾角的斜坡岩体破坏方式研究,可以达到系统评价预测斜坡稳定性的目的;通过公路开挖对不同产状岩层可能造成灾害的预期,可以采用不同的预防措施,避免大型灾害的发生。     

Kink band instability in layered structures

A recent two-dimensional prototype model for the initiation of kink banding in compressed layered structures is extended to embrace the two propagation mechanisms of band broadening and band progression. As well as interlayer friction, overburden pressure and layer bending energy, the characteristics of transverse layer compressibility and foundation stiffness are now included. Experiments on constrained layers of paper show good agreement with the predictions of angle of orientation, kink band width and post-kink load-deflection response obtained from the model.     

Thermodynamics of plastic hinges with damage

Elastic structural members are considered with plastic hinges at which damage may occur. Equations of balance of linear momentum, angular momentum and energy are obtained expressing the fact that energy may be absorbed by damage at a plastic hinge. It is shown that all the work done by the moments in bending of a plastic hinge that does not appear as heat must be absorbed by damage. The fraction of the bending work which is transformed into damage is thecoefficient of damage. In general, this coefficient is smaller than unity, which implies that the plastic hinge is a heat source. The heat source manifests itself by producing a jump discontinuity in axial heat flux and thus, in virtue of Fourier's law, a jump discontinuity in temperature gradient ensues. The general thermodynamics of the system is formulated: It is shown that agreement with the second law of thermodynamics prevails if the coefficient of damage does not exceed unity. Using the condition that a plastic hinge must break after absorbing a critical amount of damage energy, we show that a structure composed of such structural members with a finite number of plastic hinges must fail before it absorbs an infinite amount of energy through a cyclic loading and unloading program. Although the failure criterion for a single plastic hinge may be simple, the complex distribution of damage among the plastic hinges of an entire structure can make the failure criteria for a structure defy simple rules. It is also argued that the introduction of a distributed damage energy rate does not seem feasible in view of the second law of thermodynamics. This suggests that damage in a microstructure is localized rather than uniformly distributed.     

Dynamic stress chain formation in a two-dimensional particle bed

Cure cast plastic bonded explosives (PBXs) consist of relatively hard particles in a soft binder. Under compressive loading, the explosive cyrstals come into contact that causes high stress concentrations. The lines along which the crystals are loaded are called stress chains. Damage done to these particle beds during compressive loading can lead to reaction. The photoelastic effect of PMMA is exploited to examine the stress state within a two-dimensional particle bed. Stress chain development within the bed is recorded and is shown to increase the stress state within some particles while leaving others unloaded. These concentrations form early in the loading process, leading to fracture along the stress bridges and generating likely reaction initiation sites. Through material point method simulations, contact friction is shown to have a large effect on the stress distribution within the particle bed.     

Approximate analysis of progressive deformation in honeycomb structures subjected to in-plane loading

Progressive deformation of honeycomb structures subjected to in-plane loading was approximately analyzed by using the collapse modes of hexagonal unit cells. The collapse modes were categorized as freely compressive, restricted compressive, and shear. Moreover, there were five characteristic deformation patterns, namely deformation bands. Average stresses of the collapsing honeycomb models were evaluated in terms of the plastic collapse stress per hinge and total number of hinges of progressively arising deformation bands. The displacements of the models were obtained by multiplying the displacement per cell with the number of collapsed cells. The present method was used to analyze progressive deformation of typical honeycomb structures. The validity of the stress–displacement relations derived for some structures was confirmed by comparing them with finite element method (FEM) results. Our method is much simpler than FEM but just as effective.     

Failure Mechanisms of Plasterboard in Nail Pull Test Determined by X-ray Microtomography and Digital Volume Correlation

To design lightweight plasterboard and optimize the compromise between thermal resistance and mechanical strength, it is important to characterize its strength as assessed with the normative “Nail pull” test. Understanding the phenomenology of this test is the key to identifying the limiting factor in terms of load carrying capacity. In this work, the degradation mechanisms of lightweight plasterboard are analyzed via tests conducted in situ in a laboratory tomograph. Through the analysis of the kinematics by digital volume correlation, the different mechanisms at play up to failure mechanism have been identified, i.e., quasi-elastic regime, failure of the roller coating layer, core compaction and core failure. The compaction of the core by the collapse of porosity in compression is recognized as the limiting factor in terms of compressive strength and tearing resistance.     

The formation of tabular compaction-band arrays: Theoretical and numerical analysis

The bifurcation analysis of compaction banding is extended to the formation of a tabular discrete compaction-band array. This analysis, taken together with the results of finite-difference simulations, shows that the bifurcation results in the formation of intermittent loading (elastic-plastic) and unloading (elastic) bands. The obtained analytical solution relates the spacing parameter χ (the ratio between the band thickness to the band-to-band distance) to all constitutive and stress-state parameters. Both this solution and numerical models reveal strong dependence of χ on the hardening modulus h: χ increases with h reduction. The band thickness in the numerical models is mesh dependent, but in terms of mesh-zone-size varies only from ∼2 to 4 depending on the constitutive parameters and independently on the mesh resolution. The thickness of the “elementary” compaction bands in real granular materials is equal to a few grain sizes. It follows that one grid zone in the numerical models corresponds approximately to one grain in the real material. The numerical models reproduce both discrete and continuous propagating compaction banding observed in the rock samples. These phenomena were shown to be dependent on the evolution of h and the dilatancy factor with deformation.     

含层理页岩气藏水力压裂裂纹扩展规律解析分析

页岩气蕴藏在页岩层中,页岩层的层理性构造使其水力压裂裂纹扩展与常规均质储层不同.为研究页岩储层水力压裂的裂纹扩展规律,基于复变函数保角变换,得出裂纹尖端应力集中解,考虑页岩非均质、强度各向异性特点,通过比较裂纹沿各方向扩展所需的裂缝尖端水压力,推导出水力压裂裂纹垂直于最小地应力方向稳定扩展过程中在斜交层理后的扩展判据.分别定义了水力压裂裂纹在层理处起裂和沿层理扩展的弱层和岩石基体临界强度比,根据两个临界强度比确定水力压裂裂纹遇层理时在层理处起裂和沿层理扩展的层理弱面强度范围,以此表示水力压裂裂纹转向层理扩展的难易程度.通过对裂纹扩展判据的分析得出:层理起裂弱层和岩石基体临界强度比随层理走向线与第一主应力夹角和层理倾角的减小以及第三主应力和岩石基体强度的增大而增大;层理走向角小于35.26°时,层理起裂弱层和岩石基体临界强度比随第一主应力的减小以及第二主应力的增大而增大;反之,层理起裂弱层和岩石基体临界强度比随第一主应力的减小以及第二主应力的增大而减小;层理扩展弱层和岩石基体临界强度比随层理走向线与第一主应力夹角、层理倾角和地应力差的减小以及岩石基体抗拉强度的增大而增大.层理起裂条件与层理扩展条件同时满足时,水力压裂裂纹转向层理方向扩展.      

Atomistic damage mechanisms during hypervelocity projectile impact on AlN: A large-scale parallel molecular dynamics simulation study

Atomistic mechanisms of damage initiation during hypervelocity (15 km/s) impact on an AlN coating is investigated using parallel molecular-dynamics simulations involving 209 million atoms. On impact a strong shock wave is generated, which then splits into an elastic precursor and a structural phase transformation (SPT) waves, the latter driving a wurtzite to rocksalt structural transition. During its development, the SPT wave induces plastic processes in the intact wurtzite material, which in turn facilitate the nucleation and growth of brittle cracks. Specifically, the interface between the transformed (rocksalt) and untransformed (wurtzite) regions acts as a source of nanocavities and kink bands. They further interact with stress release waves reflected from the back surface and create cracks in mode I, from the nanocavities, and in mode II, from the kink band superdislocation boundary. Stresses are evaluated using a stoichiometric-preserving formula for virial local averages on inhomogeneous binary systems. Defects are analyzed using shortest-path ring statistics.     

Dimensionless design model for biaxial Cartwheel flexure hinges

Flexure hinges have been widely used in space-borne telescopes for mounting reflective optics with high surface figure requirements. To realize the three-point flexural mount of a Φ750 mm primary mirror, a Cartwheel biaxial flexural hinge composed by filleted short beams is proposed and the dimensionless design graph method for the flexural hinge is presented. The finite element analysis is performed on the flexure model to validate the proposed method. We also demonstrate the feasibility of the proposed method experimentally. The maximum relative error of the rotational stiffness between analysis, testing result, and design value is 5.0%. The proposed dimensionless design graph can be used as a design tool to determine the optimal geometry of a spatial flexure hinge rapidly.     

A study of different modes of collapse in metallic hemispherical shells resting on flat platen and compressed with hemispherical nosed indenter

The paper presents experimental and analytical studies on axial compression of aluminium spherical shells having Radius/wall thickness (R/t) ratios between 23 and 135. Quasi-static compressive load was applied centrally and with offset through a indenter having diameter of 22 mm. Testing was carried out on an INSTRON machine having 250 T capacity. Shells having different radius and wall thickness were tested, to classify their modes of collapse and their corresponding energy absorption mechanism. In experiments shells of lower R/t values were found to collapse due to formation of an inward dimple associated with a rolling plastic hinge in central as well as in offset loading. On the other hand, shells of higher R/t values were collapsed initially with formation of an axisymmetric inward dimple, but in later stage of compression showed buckling of non-symmetric shape consisting of integral number of lobes and stationary plastic hinges. The stationary hinges were formed between consecutive lobes. Experimental observations are used to propose an analytical model for prediction of load–compression and energy–compression curves. The results obtained from analytical model compared with the experimental results and found match fairly well.