An improved strain-softening constitutive model of granite considering the effect of crack deformation

This paper presents an improved strain-softening constitutive model considering the effect of crack deformation based on the triaxial cyclic loading and unloading test results.The improved model assumes that total strain is a combination of plastic,elastic,and crack strains.The constitutive relationship between the crack strain and the stress was further derived.The evolutions of mechanical parameters,i.e.strength parameters,dilation angle,unloading elastic modulus,and deformation parameters of crack,with the plastic strain and confining pressure were studied.With the increase in plastic strain,the cohesion,friction angle,dilation angle,and crack Poisson's ratio initially increase and subsequently decrease,and the unloading elastic modulus and the crack elastic modulus nonlinearly decrease.The increasing confining pressure enhances the strength and unloading elastic modulus,and decreases the dilation angle and Poisson's ratio of the crack.The theoretical triaxial compressive stress-strain curves were compared with the experimental results,and they present a good agreement with each other.The improved constitutive model can well reflect the nonlinear mechanical behavior of granite.

Degradable Plastics Are Vulnerable to Cracks

A plastic may degrade in response to a trigger.The kinetics of degradation have long been characterized by the loss of weight and strength over time.These methods of gross characterization,however,are misleading when plastic degrades heterogeneously.Here,we study heterogeneous degradation in an extreme form:the growth of a crack under the combined action of chemistry and mechanics.An applied load opens the crack,exposes the crack front to chemical attack,and causes the crack to outrun gross degradation.We studied the crack growth in polylactic acid(PLA),a polyester in which ester bonds break by hydrolysis.We cut a crack in a PLA film using scissors,tore it using an apparatus,and recorded the crack growth using a camera through a microscope.In our testing range,the crack velocity was insensitive to load but was sensitive to humidity and pH.These findings will aid the development of degradable plastics for healthcare and sustainability.

Crystal plasticity model to predict fatigue crack nucleation based on the phase transformation theory

A crystal plasticity model is developed to predict the fatigue crack nucleation of polycrystalline materials,in which the accumulated dislocation dipoles are considered to be the origin of damage.To describe the overall softening behavior under cyclic loading,a slip system-level dislocation density-related damage model is proposed and implemented in the finite element analysis with Voronoi tessellation.The numerical model is applied to calibrate the stress-strain relationship at different cycles before fatigue crack nucleation.The parameters determined from the numerical analysis are substituted into a modified phase transformation model to predict the critical fatigue crack nucleation cycle.Comparing with the experimental results of Sn-3.0Ag-0.5Cu(SAC305)alloy and P91 steel,the proposed method can describe the constitutive behavior and predict the fatigue crack nucleation accurately.

Elastic-plastic analysis of antiplane crack near crack surface region

The elastic-plastic stress distribution and the elastic-plastic boundary con- figuration near a crack surface region are significant but hard to obtain by means of the conventional analysis. A crack line analysis method is developed in this paper by consid- ering the crack surface as an extension of the crack line. The stresses in the plastic zone, the length, and the unit normal vector of the elastic-plastic boundary near a crack surface region are obtained for an antiplane crack in an elastic-perfectly plastic solid. The usual small scale yielding assumptions are not needed in the analysis.

General forms of elastic-plastic matching equations for mode-Ⅲ cracks near crack line

Crack line analysis is an effective way to solve elastic-plastic crack problems. Application of the method does not need the traditional small-scale yielding conditions and can obtain sufficiently accurate solutions near the crack line. To address mode- Ⅲ crack problems under the perfect elastic-plastic condition, matching procedures of the crack line analysis method axe summarized and refined to give general forms and formulation steps of plastic field, elastic-plastic boundary, and elastic-plastic matching equations near the crack line. The research unifies mode-III crack problems under different conditions into a problem of determining four integral constants with four matching equations. An example is given to verify correctness, conciseness, and generality of the procedure.

Finite deformation analysis of crack tip fields in plastically compressible hardening–softening–hardening solids

Crack tip fields are calculated under plane strain small scale yielding conditions. The material is characterized by a finite strain elastic-viscoplastic constitutive relation with various hardening-softening-hardening hardness functions. Both plastically compressible and plastically incompressible solids are considered. Displacements corresponding to the isotropic linear elastic mode I crack field are prescribed on a remote boundary. The initial crack is taken to be a semi-circular notch and symmetry about the crack plane is imposed. Plastic compressibility is found to give an increased crack opening displacement for a given value of the applied loading. The plastic zone size and shape are found to depend on the plastic compressibility, but not much on whether material softening occurs near the crack tip. On the other hand, the near crack tip stress and deformation fields depend sensitively on whether or not material softening occurs. The combination of plastic compressibility and softening (or softening-hardening) has a particularly strong effect on the near crack tip stress and deformation fields.

Plastic analysis of the crack problem in two-dimensional decagonal Al-Ni-Co quasicrystalline materials of point group 10,■

The fundamental plastic nature of the quasicrystalline materials remains an open problem due to its essential complicacy. By developing the proposed generalized cohesive force model, the plastic deformation of crack in point group 10, 10 decagonal quasicrystals is analysed strictly and systematically. The crack tip opening displacement （CTOD） and the size of the plastic zone around the crack tip are determined exactly. The quantity of the crack tip opening displacement can be used as a parameter of nonlinear fracture mechanics of quasicrystalline material. In addition, the present work may provide a way for the plastic analysis of quasicrystals.

GENERAL FORM OF MATCHING EQUATION OF ELASTIC-PLASTIC FIELD NEAR CRACK LINE FOR MODE I CRACK UNDER PLANE STRESS CONDITION

Crack line field analysis method has become an independent method for crack elastic-plastic analysis, which greatly simplifies the complexity of crack elastic-plastic problems and overcomes the corresponding mathematical difficulty. With this method, the precise elastic-plastic solutions near crack lines for variety of crack problems can be obtained. But up to now all solutions obtained by this method were for different concrete problems, no general steps and no general form of matching equations near crack line are given out. With crack line analysis method, this paper proposes the general steps of elastic plastic analysis near crack line for mode I crack in elastic-perfectly plastic solids under plane stress condition, and in turn given out the solving process and result for a specific problem.

EXACT SOLUTIONS OF NEAR CRACK LINE FIELDS FOR MODE I CRACK UNDER PLANE STRESS CONDITION IN AN ELASTIC－PERFECTLY PLASTIC SOLID

The near crack line analysis method has been used in the present paper,The classical small scale yielding conditions have been completely abandoned in the analyses and one inappropriate matching condition used to be used at the elasticplastic boundary has been corrected.The reasonable solution of the plastic stresses near the crack line region has been established.By matching the plastic stresses with the exact elastic stresses at the elastic-plastic boundary,the plastic stresses the length of the plastic zone and the unit normal vector of the elastic-plastic boundary near the crock line region have been obtained for a mode I crack under uniaxial tension,as well as a mode I crack under biaxial tension,which shows that for both conditions the plastic stress componentsσy, and σsy.he length of the plastic zone and the unit normal vector of the elastic-plastic boundary are quite the same while the plastic stress σs is different.

Numerical Simulation and Experimental Studies on Elastic-Plastic Fatigue Crack Growth

A elastic-plastic fatigue crack growth(FCG)finite element model was developed for predicting crack growth rate under cyclic load.The propagation criterion for this model was established based on plastically dissipated energy.The crack growth simulation under cyclic computation was implemented through the ABAQUS scripting interface.The predictions of this model are in good agreement with the results of crack propagation experiment of compact tension specimen made of 304 stainless steel.Based on the proposed model,the single peak overload retardation effect of elastic-plastic fatigue crack was analyzed.The results shows that the single peak overload will reduce the accumulation rate of plastic energy dissipation of elements at crack tip plastic zone,so that crack growth will be arrested.The crack growth rate will not recover until the crack tip exceed the affected region.Meanwhile,the crack growth rate is mainly determined by the amplitude rather than the mean load under the condition of small scale yielding.The proposed model would be helpful for predicting the growth rate of mode I elastic-plastic fatigue crack.

Fatigue Crack Propagation Analysis of Orthotropic Steel Bridge with Crack Tip Elastoplastic Consideration

Due to the complex structure and dense weld of the orthotropic steel bridge deck(OSBD),fatigue cracks are prone to occur in the typical welding details.Welding residual stress(WRS)will cause a plastic zone at the crack tip.In this paper,an elastoplastic constitutive model based on the Chaboche kinematic hardening model was introduced,and the extended finite element method(XFEM)was used to study the influence of material elastoplasticity and crack tip plastic zone on the law of fatigue crack propagation.By judging the stress state of the residual stress field at the crack tip and selecting different crack propagation rate models to investigate the crack propagation law when plastic deformation was considered,the propagation path and propagation rate of fatigue crack of the OSBD were obtained.The results show that,whether the residual stress field is considered or not,the plastic deformation at the crack tip will not cause the obvious closure of the fatigue crack at the U-rib toe during the crack propagation process,but will significantly affect the crack propagation path.When material plasticity is considered,the propagation angle of fatigue crack at the U-rib toe basically remains unchanged along the short-axis direction of the initial crack,but is going up along the long-axis direction,and the crack tip plastic zone inhibits the propagation of the crack tip on one side.Compared with linear elastic materials,the crack propagation law considering material plasticity is more consistent with that in actual bridge engineering.In terms of the propagation rate,if the residual stress field is not considered,the fatigue crack propagation rate at U-rib toe with plasticity considered is slightly higher than that without plasticity considered,because plastic deformation will affect the amplitude of energy release rate.When considering the WRS field,the fatigue crack propagation rate at U-rib toe is increased due to the combined actions of plastic deformation and stress ratio R.

Alternative Diesel Grade Fuel Transformed from Polypropylene (PP) Municipal Waste Plastic Using Thermal Cracking with Fractional Column Distillation

Day by day worldwide use of plastics is increasing because of their light weight and durable characteristics. Waste plastics are major environmental problems all over the world. Waste plastics are not bio-degradable, it remains in the landfill for a long period of time causing vegetation and aquatic ecosystem dilemmas. Abandoned waste plastic thrown into the ocean causes friction of ocean waves and then broken down by sunlight into small pieces and takes the shape of plastic like soup. Aquatic organism mistakes the plastic soup as their food and can’t digest, either they die or through food chain it affects human health. To avoid severe environmental degradation problems of waste plastics some countries and big cities banned or restricted the use of plastic products. The worldwide generation of waste plastics is approximately 280 million tons/year. All most all of these waste plastics are dumped either in land or ocean. City municipalities spend huge amount of money each year just to dispose of these waste plastics into landfill because most waste plastics are not recycled. When the waste plastics are subjected to incineration, they release harmful toxic gas into the environment causing severe pollution. These waste plastics gradually enhance the hazardous environmental problems. Generally plastics are made from crude oil, however crude oil is a very limited natural resource and non-renewable. Every year millions of barrels of crude oil are to produce the waste plastics and when plastics are discarded after use the energy source is lost. A new developed technology plan minimizes the environment pollution problems simultaneously boost up energy sector by renovating the waste plastics into high energy content fuel. The produced fuel is obtained using a unique thermal degradation of waste plastics and converting them into hydrocarbon fuel like materials. Preliminary tests proved that this fuel burns cleaner and the production cost is very low. Unique production setup demonstrated to produce 93% fuel from waste plastic in the pilot scale. The Fuel produced has been tested and proven to work on majority types of internal combustion engines. This technology utilized can avoid waste plastic pollution problem worldwide by the implementation of newly developed technology. Through the utilization of the technology the use of reliable plastics won’t need to be banned and serve as a very reliable alternate source of energy. The technology will also help reduce a significant amount of import oil from foreign countries and help provide a steady economy.

Plastic deformation mechanism transition of Ti/Ni nanolaminate with pre-existing crack:Molecular dynamics study

Tensile behaviors of Ti/Ni nanolaminate with model-I crack are investigated by molecular dynamics simulations.The Ti/Ni nanolaminates with center crack either in Ti layer or in Ni layer under different loading directions are utilized to systematically study the mechanical performance of the cracked material.The results indicate that pre-existing crack dramatically changes the plastic deformation mechanism of the Ti/Ni nanolaminate.Unlike the initial plastic deformation originating from the interface or weak Ti layer of the crack-free samples,the plastic behavior of cracked Ti/Ni nanolaminate first occurs at the crack tip due to the local stress concentration.Subsequent plastic deformation is dominated by the interaction between the crack and interface.The Ti/Ni interface not only impedes the movement of the initial plastic deformation carriers(dislocation,slip band,and deformation twinning)from the crack tip,but also promotes the movement of interfacial dislocations in the tension process.Microstructure evolution analysis further confirms that the plastic deformation mechanism transition is ascribed to the orientation-dependent tensile behavior at the crack tip,which is intrinsically attributed to the anisotropy of the certain crystal structure and loading direction of the cracked Ti/Ni nanolaminate.In addition,by analyzing the effects of different plastic deformation carriers on crack propagation in specific crystal,it can be discovered that the interfacial dislocations moving towards the crack tip can further promote the crack growth.

CRACK INITIATION AND STEADY PROPAGATION OF ELASTIC-PLASTIC MATERIALS IN PLANE STRESS CONDITION

The crack tip stress-strain fields of the elastic-plastic cracked specimens have been analyzed using finite element calculations.The crack initiation and steady propagation behaviours have also been investigated by means of slip line pattern etching technique and mechanical tests. The results show that there are HRR near field and distant field in the crack tip region,and the later depends on the specimen configuration.The crack initiation behaviour is controlled by a single parameter J.In contrast,the steady crack propagation is affected by the distant strain field and can not be described by single parameter only.

Elastic-plastic analytical solution for centric crack loaded by two pairs of point shear forces in finite plate

The near crack line analysis method was used to investigate a centric crack loaded by two pairs of point shear forces in a finite plate, and the analytical solution was obtained. The solution includes the unit normal vector of the elastic-plastic boundary near the crack line, the elastic-plastic stress fields near the crack line, the variations of the length of the plastic zone along the crack line with an external load, and the bearing capacity of a finite plate with a centric crack loaded by two pairs of point shear forces. The results are sufficiently precise near the crack line because the assumptions of small scale yielding theory have not been made and no other assumptions are taken.

SOME POSSIBLE ALTERNATIVE SOLUTIONS OF NEAR TIP FIELDS FOR STEADY CRACK GROWTH IN ELASTIC PERFECTLY-PLASTIC MEDIA

Some possible alternative solutions of near-tip fields are studied for plane-strain Mode-I qua- si-static steady crack growth in incompressible(v=1/2)elastic perfectly-plastic media.A group of four-sector so- lutions and a three-sector solution in which the elastic-unloading region vanishes are given.Stress functions,plas- tic flow factors and plastic strains in each region are also given.

PLASTIC ZONE OF SEMI-INFINITE CRACK IN PLANAR KAGOME AND TRIANGULAR LATTICES

The fracture investigations of the planar lattices made of ductile cell walls are currently limited to bending-dominated hexagonal honeycomb. In this paper, the plastic zones of stretching-dominated lattices, including Kagome and triangular lattices, are estimated by analyzing their effective yield loci. The normalized in-plane yield loci of these two lattices are almost identical convex curves enclosed by 4 straight lines, which is almost independent of the relative density but is highly sensitive to the principal stress directions. Therefore, the plastic zones around the crack tip of Kagome and triangular are estimated to be quite different to those of the continuum solid and also hexagonal lattice. The plastic zones predictions by convex yield surfaces of both lattices are validated by FE calculations, although the shear lag region caused by non-local bending effect in the Kagome lattice enlarges the plastic zone in cases of small ratio of rp/l.

STEADY GROWTH OF CRACKS IN COMPRESSIBLE ELASTIC-PLASTIC MEDIA

Based on the theoretical framework for crack growth analysis provided by Gao and Hwang, the 5-sector soiution of near-tip fields of mode-I cracks growing quasi-statically and steadily in compressible elastic perfectly plastic materials is obtained.As Poisson's ratio v tends to 1/2,the 5-sector solution degener- ates to the 4-sector solution of near-tip fields of crack growth in incompressible elastic perfectly plastic materials.

NEAR-TIP FIELDS FOR A CRACK GROWING ALONG AN ELASTIC PERFECTLY PLASTIC INTERFACE

The stress and deformation fields near the tip of an anti-plane crack growing quasi-statically along an interface of elastic perfectly plastic materials are given in this paper. A family of solutions for the growing crack fields is found covering all admissible crack line shear stress ratios.

THE FULLY PLASTIC J-INTEGRAL OF CORNER CRACKS AT A HOLE IN A PLATE

The line-spring model of surface cracks is applied to the fully plastic analysis of corner cracks at a hole in a plate. The generalized fully plastic constitutive relations and the fully plastic J-integral, as well as its coefficients in polynomial expressions are given. The model obtained is incorporated into a finite element program. The corner cracks at a hole in a plate subjected pure tensions are calculated by the present model. The fully plastic J-integral is then estimated. The results obtained show that the line-spring model is effective for the analysis of corner cracks. The influence of the crack depth and the hardening exponent on the fully plastic J-integral is also discussed.