A simple cohesive zone model that generates a mode-mixity dependent toughness

A simple, mode-mixity dependent toughness cohesive zone model (MDG_c CZM) is described. This phenomenological cohesive zone model has two elements. Mode I energy dissipation is defined by a traction–separation relationship that depends only on normal separation. Mode II (III) dissipation is generated by shear yielding and slip in the cohesive surface elements that lie in front of the region where mode I separation (softening) occurs. The nature of predictions made by analyses that use the MDG_c CZM is illustrated by considering the classic problem of an elastic layer loaded by rigid grips. This geometry, which models a thin adhesive bond with a long interfacial edge crack, is similar to that which has been used to measure the dependence of interfacial toughness on crack-tip mode-mixity. The calculated effective toughness vs. applied mode-mixity relationships all display a strong dependence on applied mode-mixity with the effective toughness increasing rapidly with the magnitude of the mode-mixity. The calculated relationships also show a pronounced asymmetry with respect to the applied mode-mixity. This dependence is similar to that observed experimentally, and calculated results for a glass/epoxy interface are in good agreement with published data that was generated using a test specimen of the same type as analyzed here.     

Collapse failure in dry clay soils caused by tine implements

The relation between forces applied to the soil and the resultant soil reaction was studied in dry clay soils under a quasi-static condition. As a tine advanced in dry compact clay soils at 5.2% dry basis moisture content, masses of soil collapsed one by one in front of the tine. The horizontal and vertical components of soil resistance measured were cyclic and in phase, with distinct peak and trough values. The peak values and trough values indicated the soil stress conditions before and immediately after each failure occurred. The frequency of failure depended on the size of the tine. The magnitude of the peak values depended on level of compaction and trough values on density of collapsed mass. The paper presents the details of observations.     

Prediction of soil structures produced by tillage

A statistical method for describing the distribution of aggregates and voids within tilled soil is used as the basis for a prediction technique. Transforms of aggregate-void and void-void transition probabilities are used in such a way that factors can be defined which describe how the soil structure differs under a range of circumstances. A standard structure is defined for a given soil as that which is produced at the 5 cm depth by one pass of a set of tines working at 10 cm depth when tillage is done at a speed of 1.4 m/s in soil at a water content equal to the plastic limit and which has previously grown a cereal crop. Factors are defined which describe deviations from this standard structure as a function of depth in the tilled layer, implement type, previous use of the soil, number of implement passes, water content at time of tillage, and subsequent compaction of thettilled layer. Application of the inverse transform then enables estimates of the distributions of aggregates and voids in the tilled layer to be predicted for required, specified conditions.     

A unified potential-based cohesive model of mixed-mode fracture

A generalized potential-based constitutive model for mixed-mode cohesive fracture is presented in conjunction with physical parameters such as fracture energy, cohesive strength and shape of cohesive interactions. It characterizes different fracture energies in each fracture mode, and can be applied to various material failure behavior (e.g. quasi-brittle). The unified potential leads to both intrinsic (with initial slope indicators to control elastic behavior) and extrinsic cohesive zone models. Path dependence of work-of-separation is investigated with respect to proportional and non-proportional paths—this investigation demonstrates consistency of the cohesive constitutive model. The potential-based model is verified by simulating a mixed-mode bending test. The actual potential is named PPR (Park-Paulino-Roesler), after the first initials of the authors’ last names.     

A thermodynamics-based cohesive model for interface debonding and friction

A constitutive model for interface debonding is proposed which is able to account for mixed-mode coupled debonding and plasticity, as well as further coupling between debonding and friction including post-delamination friction. The work is an extension of a previous model which focuses on the coupling between mixed-mode delamination and plasticity. By distinguishing the interface into two parts, a cracked one where friction can occur and an integral one where further damage takes place, the coupling between frictional dissipation and energy loss through damage is seamlessly achieved. A simple framework for coupled dissipative processes is utilised to derive a single yield function which accurately captures the evolution of interface strength with increasing damage, for both tensile and compressive regimes. The new material model is implemented as a user-defined interface element in the commercial package ABAQUS and is used to predict delamination under compressive loads in several test cases.     

A micromechanical model of elastoplastic and damage behavior of a cohesive geomaterial

The present study is devoted to the development and validation of a nonlinear homogenization approach of the mechanical behavior of Callovo-Oxfordian argillites. The material is modeled as an heterogeneous composite composed of an elastoplastic clay matrix and of linear elastic or elastic damage inclusions. The macroscopic constitutive law is obtained by adapting the incremental method proposed by Hill [Hill, R., 1965. Continuum micro-mechanics of elastoplastic polycrystals. J. Mech. Phys. Solids 13, 89–101]. The approach consists in formulating the macroscopic tangent operator of the material by considering the nonlinear local behavior of each phase. Due to the matrix/inclusion morphology of the microstructure of the argillite, a Mori–Tanaka scheme is considered for the localization step. The developed model is first compared to Finite Element calculations and then validated and applied for the prediction of the macroscopic stress–strain responses of argillites.     

A simple model for the flow and temperature distribution analysis in a manifold-shaped direct cooling system

A fluid dynamic and thermal analysis has been carried out for the calculation of pressure, velocity and temperature distribution in a manifold-shaped cooling system of varying geometrical characteristics.A physical model of the general problem has been developed and solved by a numerical procedure. The results obtained are compared with some available experimental data on a box-shaped manifold, arranged with straight and inclined branches.     

Electro-hydraulic tillage depth control system for rotary implements mounted on agricultural tractor Design and response experiments of control system

A tillage depth control system for rotary implements mounted on an agricultural tractor was designed and constructed to improve accuracy of tillage depth. The control system was composed of five main units: (1) a detecting unit to measure the tilting angle (position) of the lift arm, the pitching angle of the tractor and heights of sensors from ground surface, (2) a controlling unit, (3) a hydraulic unit to operate a three-point hitch linkage by a lift arm cylinder, (4) a three-point hitch linkage and rotary implements, and (5) a setting unit to put the reference tillage depth and a dead zone into the control circuit. The tillage depth was controlled by an on/off operation of a solenoid valve, of which time was proportional to the controlling time. Experiments to evaluate the response characteristics of the control system were conducted under various engine speeds, i.e. various flow rates of hydraulic oil, various tillage depths and some input frequencies. The results of the response experiments of the control system are discussed in this paper.     

A harmonic model of hydrodynamic forces produced by a flapping fin

The hydrodynamic control laws of unsteady fins inspired by swimming and flying animals are considered. A controller based on cycle-averaged forces requires a bandwidth lower than the flapping frequency, with correspondingly slow reactions to disturbances or commands in order to avoid undesirable feedback from the oscillating fins. A harmonic model of the periodic thruster forces was empirically found using a mechanical fin flapping in roll and pitch in hover, in uniform flow, and under various kinematic conditions. A multi-fin vehicle could use this model to account for the dominant non-linearities and minimize undesirable motions through coordinated control of individual fins.     

Prediction of transient displacement, velocity, and force on projectiles penetrating cohesive soils

A closed-form solution is developed for predicting transient displacement, velocity, and force as well as residual displacement and duration for both flat and pointed projectiles penetrating cohesive soils. Because transient response can be represented as a 3 parameter space of nondimensional numbers, displacement, velocity, and force are each presented in a single graph. Experimental test data for different soils and penetrator contours are used to demonstrate the validity of both transient and residual responses. Of great importance in this solution and soil dynamics in general is the advancement of a hypothesis for the dynamic interaction of intergranular stress, pore water pressure, and pore air pressure in the resisting force that retards penetration. Because fundamental dynamic pore pressure theory is used to develop this analysis, basic soil properties (cohesive yield strength, density, and degree of saturation) are used to characterize the cohesive soil.     

A comparison of cohesive zone modeling and classical fracture mechanics based on near tip stress field

A mode III crack with a cohesive zone in a power-law hardening material is studied under small scale yielding conditions. The cohesive law follows a softening path with the peak traction at the start of separation process. The stress and strain fields in the plastic zone, and the cohesive traction and separation displacement in the cohesive zone are obtained. The results show that for a modest hardening material (with a hardening exponent N = 0.3), the stress distribution in a large portion of the plastic zone is significantly altered with the introduction of the cohesive zone if the peak cohesive traction is less than two times yield stress, which implies the disparity in terms of the fracture prediction between the classical approach of elastic–plastic fracture mechanics and the cohesive zone approach. The stress distributions with and without the cohesive zone converge when the peak cohesive traction becomes infinitely large. A qualitative study on the equivalency between the cohesive zone approach and the classical linear elastic fracture mechanics indicates that smaller cracks require a higher peak cohesive traction than that for longer cracks if similar fracture initiations are to be predicted by the two approaches.     

A theoretical model of matrix cracking in composite laminates under thermomechanical loading

A theoretical approach is presented for analyzing the ply cracking in general symmetric laminates subjected to any combination of in-plane mechanical loading and uniform temperature changes. The equivalent constraint model proposed by the authors in a previous work is used to account for the cracking interaction between laminae in the laminates. By using a superposition scheme and the stress field solutions the energy release rate for a ply cracking is explicitly expressed as a function of stiffness reduction parameters of the laminates. The ratio of mode I to mode II is introduced for construction of the fracture criterion. The effects of the laminate parameters and the crack spacing on the energy release rate and the mode mixity are illustrated. Finally, the model is used to predict the thermomechanical load for the first-ply-cracking. Project supported by the National Natural Science Foundation of China (No. 19972076) and the Germen Research Foundation (DFG).     

Deformation produced by a simple tensile load in an isotropic elastic body

It is shown that a simple tensile load produces a simple extension provided the empirical inequalities (Truesdell and Noll [1], eqn. 51.27) hold.     

The creep behavior of simple structures with a stress range-dependent constitutive model

High temperature design remains an issue for many components in a variety of industries. Although finite element analysis for creep is now an accessible tool, most analyses outside the research domain use long standing and very simple constitutive models—in particular based on a power law representation. However, for many years, it has been known that a range of materials exhibit different behaviors at low and moderate stress levels. Recently, studies of the behavior of high temperature structures with such a stress range-dependent constitutive model have begun to emerge. The aim of this paper is to examine further the detailed behavior of simple structures with a modified power law constitutive model in order to instigate a deeper understanding of such a constitutive model’s effect on stress and deformation and the implications for high temperature design. The structures examined are elementary—a beam in bending and a pressurized thick cylinder—but have long been used to demonstrate the basic characteristics of nonlinear creep.     

The dynamics of a simple model for a thixotropic yield stress fluid

We study the dynamics of a model for thixotropic yield stress fluids which was recently proposed in [1]. This is based on the partially extended convected model (PEC), modified to allow for a non-zero shear stress limit for large shear rates (PECR), and combined with a Newtonian solvent to enable yielding to homogeneous shear flow (PECR-N) under a prescribed shear stress. We define ? to be the ratio of retardation time to relaxation time and focus on the limit ? → 0. Multiple time scales arise and the solutions are investigated with perturbation methods, in conjunction with direct computation of the full set of equations. Both PEC-N and PECR-N capture the experimentally observed phenomenon that the value of yield stress depends on the observation time. For the PECR-N model, we find transient solutions that are not expected from prior work on the PEC-N model, such as blow-up in finite time on the slow manifold, and yielded time-periodic flow.     

Failure mode transitions in RC beams: A cohesive/overlapping crack model application

The analysis of reinforced concrete beams in flexure taking into account the nonlinear behaviour of concrete is addressed by a numerical approach based on the Cohesive-Overlapping Crack Model. An extensive experimental research has been proposed by Bosco and Carpinteri (Scale effects and transitional phenomena of reinforced concrete beams in flexure. ESIS Technical Committée 9 Round Robin proposal, 1993), Bosco et al. (Scale effects and transitional failure phenomena of reinforced concrete beams in flexure. Report to ESIS Technical Committée 9, 1996) and El-Khatieb (Transizione di scala duttile-fragile per le travi in calcestruzzo armato. PhD Thesis, 1997) in order to obtain a rational explanation for failure transitional phenomena of RC beams by varying steel percentage and/or beam slenderness and/or beam size-scale. In the present paper, collapse mechanisms due to concrete tensile cracking, concrete compressive crushing and steel yielding and/or slippage are analysed and a numerical vs. experimental comparison is presented in order to validate the proposed model.     

Size effect in quasibrittle failure: Analytical model and numerical simulations using cohesive zone model

The recent rewriting of the Ba?ant’s size effect law (Morel, 2008) which has suggested the existence of an additional asymptotic regime for intermediate structure sizes is now compared to numerical simulations of fracture of geometrically similar notched structures of different sizes extending over 2.4 decades. The quasibrittle fracture behavior is simulated through cohesive zone model (bilinear softening) using a constant set of cohesive parameters whatever the specimen size D is. The R-curves resulting from the load–displacement responses are estimated and appear as size-independent. On this basis, the different asymptotic regimes expected for the size effect on fracture properties at peak load such as the relative crack length, the resistance to crack growth and the nominal strength are shown in fair agreement with the size effect observed on the results obtained from numerical simulations.