Analytical Model and Experimental Verification of the Interfacial Peeling Strength of Electrodes

Background

The interfacial peeling strength of lithium-ion battery electrodes is a very important mechanical property that significantly affects the electrochemical performance of battery cells.

Objective

To characterize the interfacial peeling strength of an electrode, an analytical model based on the energy balance principle is established by considering the state of charge (SOC), the energy release rate, the tensile stiffness, and the peeling angle.

Methods

Uniaxial tensile tests and 180-degree peeling tests are conducted to determine the Young’s modulus and the interfacial peeling strengths of electrodes at different SOCs, respectively. The experimental data serve as a validation of the accuracy of the analytical model.

Results

The interfacial peeling strength of the electrode shows a strong reliance on many factors. Specifically, the interfacial peeling strength increases with the SOC and the energy release, and decreases with the peeling angle. When the tensile stiffness of the active layer equals that of the current collector, the interfacial peeling strength has a maximum value.

Conclusions

By comparing with experimental data of the 180-degree peeling test, the model prediction shows excellent agreement at different SOCs, and the analytical model established in this paper can be used to guide and assess the interfacial properties of electrodes for industry.

     

On Finite Shear

If a pair of material line elements, passing through a typical particle P in a body, subtend an angle Θ before deformation, and Θ+γ after deformation, the pair of material elements is said to be sheared by the amount γ. Here all pairs of material elements at P are considered for arbitrary deformations. Two main problems are addressed and solved. The first is the determination of all pairs of material line elements at P which are unsheared. The second is the determination of that pair of material line elements at P which suffers the maximum shear. All unsheared pairs of material elements in a given plane π(S) with normal S passing through P are considered. Provided π(S) is not a plane of central circular section of the C-ellipsoid at P (where C is the right Cauchy-Green strain tensor), it is seen that corresponding to any material element in π(S) there is, in general, one companion material element in π(S) such that the element and its companion are unsheared. There are, however, two elements in π(S) which have no companions. We call their corresponding directions \textit{limiting directions.} Equally inclined to the direction of least stretch in the plane π(S), the limiting directions play a central role. It is seen that, in a given plane π(S), the pair of material line elements which suffer the maximum shear lie along the limiting directions in π(S). If Θ _L is the acute angle subtended by the limitig directions in π(S) before deformation, then this angle is sheared into its supplement π−Θ _L so that the maximum shear γ^*;(S) is γ^*=π− 2 Θ _L . If S is given and C is known, then Θ _L may be determined immediately. Its calculation does not involve knowing the eigenvectors or eigenvalues of C. When all possible planes through P are considered, it is seen that the global maximum shear γ^* _G occurs for material elements lying along the limiting directions in the plane spanned by the eigenvectors of C corresponding to the greatest principal stretch λ₃ and the least λ₁. The limiting directions in this principal plane of C subtend the angle and . Generally the maximum shear does not occur for a pair of material elements which are originally orthogonal. For a given material element along the unit vector N, there is, in general, in each plane π(S passing through N at P, a companion vector M such that material elements along N and M are unsheared. A formula, originally due to Joly (1905), is presented for M in terms of N and S. Given an unsheared pair π(S), the limiting directions in π(S) are seen to be easily determined, either analytically or geometrically. Planar shear, the change in the angle between the normals of a pair of material planar elements at X, is also considered. The theory of planar shear runs parallel to the theory of shear of material line elements. Corresponding results are presented. Finally, another concept of shear used in the geology literature, and apparently due to Jaeger, is considered. The connection is shown between Cauchy shear, the change in the angle of a pair of material elements, and the Jaeger shear, the change in the angle between the normal N to a planar element and a material element along the normal N. Although Jaeger's shear is described in terms of one direction N, it is seen to implicitly include a second material line element orthogonal to N. Accepted: May 25, 1999     

Basic Geometrical Properties of Optimal Flexural Force Transmission Fields

Abstract

On the basis of theories of optimal design by Masur, Prager and Shield, kinematic optimality conditions for elastic and elastic-plastic plane flexural systems of maximum strength and maximum stiffness were previously derived. In the present paper, general geometrical properties of moment and displacement fields in various types of optimal regions are outlined with a view to constructing optimal solutions for any arbitrary set of boundary conditions.     

γ-p-S a -S m -N Surface theory and two-dimensional reliability miner rule for fatigue reliability-based design

First of all, the concept of γ-p-S_a-S_m-N (confidence level-relabilitystress amplitude-stress mean-fatigue life) surface is presented. Then the formulas of p-S_a-S_m-N surface and γ-p-S_a-S_m-N surface are derived. In addition, fatigue strength distribution function and two-dimensional reliability Miner rule are obtained. At last, an example is given. Foundation item: the National Natural Science Foundation of China (19672051)     

Shear and Bending Response of a Rigid Plastic Circular Plate Struck Transversely by a Mass*

ABSTRACT

A theoretical analysis is presented for the dynamic plastic behavior of a fully clamped rigid, perfectly plastic circular plate struck transversely by a rigid mass at the center. It is shown that the maximum permanent transverse deformation predicted by a theoretical solution, with combined transverse shear and bending, is similar to that from a bending-only solution when the ratio of shear strength to bending capacity υ is sufficiently large. However, when the strength parameter υ is small, the transverse shear deformation dominates the response and the maximum deformation from a combined shear and bending solution increases sharply with a decrease in υ. It is also found that the transverse shear deformation becomes more important with an increase in the dimensionless mass ratio β and is sensitive to the dimensionless radius ρ₀ of the impact area.     

Convex Analysis of the Eigenvalues of a 3D Second-Order Symmetric Tensor

Within the framework of nonsmooth convex analysis, the subdifferentials of the maximum eigenvalue and the negative of the minimum eigenvalue of a three-dimensional second-order symmetric tensor A are determined for all possible cases in an explicit and coordinate-free way. In particular, the expressions obtained for the subdifferentials show that: (i) An eigenvalue of A is differentiable if and only if it is simple; (ii) the maximum eigenvalue of A is subdifferentiable when it is double or triple; (iii) the negative of the minimum eigenvalue of A is subdifferentiable when it is double or triple. These results can be applied directly to elasticity and continuum mechanics where three-dimensional second-order symmetric tensor eigenvalues are frequently involved.     

Die umkehrung der stabilitätssätze von Lagrange-Dirichlet und Routh

Summary The Lagrange-Dirichlet theorem states that the equilibrium position of a discrete, conservative mechanical system is stable if the potential energy U(q) assumes a minimum in this position. Although everything seems to indicate that the equilibrium is always unstable in case of a maximum of the potential energy, this has yet to be proven. In all existing instability theorems the function U(q) has to satisfy additional requirements which are very restrictive.In this paper instability is proved in the case of a maximum of U(q)C ², without further restrictions. The instability follows directly from the existence of certain types of motions which are not found as solutions of differential equations, but as the solutions of a variational problem. Existence theorems are given for the variational problem, based on a result found by Carathéodory.In similar way an inversion of Routh's theorem on the stability of steady motions in systems with cyclic coordinates is also given. The result obtained here is not as general as the inversion of the Lagrange-Dirichlet theorem because the equations of motion are of a more complex type.

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Vorgelegt von C. Truesdell

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Von der Fakultät für Mathematik der Universität Karlsruhe (TH) angenommene Habilitationsschrift.     

On the Optimal Shape of an Elastic-Plastic Column

Abstract

The problem of maximizing the buckling load of a plastic column of given volume, length, and material is studied. The governing equations are derived by means of the calculus of variations, and a parametric constraint on the maximum permissible stress is included in the analysis. The general problem is solved numerically, and the results obtained for some special cases, e.g., elastic columns, are shown to be in agreement with those found by previous investigators.     

Stretching Graphene to 3.3% Strain Using Formvar-Reinforced Flexible Substrate

Background

As a one-atom-thick material, the mechanical loading of graphene in large scale remains a challenge, and the maximum tensile strain that can be realized is through a flexible substrate, but only with a value of 1.8% due to the weak interfacial stress transfer.

Objective

Aims to illustrate the interface reinforcement brought by formvar resins as a buffering layer between graphene and substrates.

Methods

Single crystal graphene transferred to different substrates, applied with uniaxial stretching to compare the interface strength, and finite element analysis was performed to simulate tensile process for studying the influence of Poisson’s ratio of the buffering layer for interface reinforcement.

Results

In this work we use formvar resins as a buffering layer to achieve a maximum uniaxial tensile strain of 3.3% in graphene, close to the theoretical limit (3.7%) that graphene can achieve by flexible substrate stretching. The interface reinforcement by formvar is significantly higher than that by other polymers, which is attributed to the liquid–solid phase transition of formvar for more conformal interfacial contact and its suitable Poisson’s ratio with graphene to avoid its buckling along the transverse direction.

Conclusions

We believe that these results can provide guidance for the design of substrates and interfaces for graphene loading, as well as the support for mechanics analysis of graphene-based flexible electronic devices.

     

Deflection Analysis of Elastic-Plastic Frames at Shakedown

ABSTRACT

A method is presented providing an upper bound solution to the maximum deflections which may occur in elastic-plastic frames under loadings that vary arbitrarily within prescribed limits.

The problem is reduced to linear programming; a numerical example is given. The results show that the theory of shakedown remains valid even for very low values of the safety factor against incremental collapse.     

Infinitesimal elastic stability of homogeneous deformations and the zero moment condition

We investigate the relationships between the infinitesimal elastic stability of homogeneous deformations and the zero moment condition. Under dead loading, for physically reasonable constitutive assumptions, we find that if the infinitesimal deformation satisfies the zero moment condition, it is stable under a very weak condition, one which includes an all-round compressive state. We show further that for a given stretching D the deformation L with the zero moment condition is the minimum (maximum) stable deformation in the state 53-1. Here 53-2 and t _a, a=1, 2, 3, are the principal Biot and Cauchy stresses, respectively. Finally, we examine stability when the prescribed traction rate is controlled such that the zero moment condition is satisfied for any deformation.     

Dual extremum principles relating to optimum beam design

Of concern is a cantilever beam resting on an elastic foundation and supporting a load at the free end. The beam is of rectangular cross section and of constant height but variable width. It is required to taper the beam for maximum strength. This means that the beam is to support a maximum vertical load W at the free end when the free end is given unit deflection. The constraint is that the weight of the beam should not exceed a given bound K. It is shown that the optimum taper should be so chosen that the curvature of the beam is constant. This yields the solution of the problem in terms of explicit formulas. For more general constraints, an inequality is found which gives upper and lower bounds for the maximum load W even though explicit formulas are not available.This paper was prepared under Research Grant DA-ARO-D-31-124-71-G17, U.S. Army Research Office (Durham).     

Identities in Finite Strain

First of all the deformation is considered of two infinitesimal material line elements lying along vectors M,N emanating from a particle at X in a body. For all M,N lying in a given plane, an identity is derived relating the stretches along M,N and the angles of the pair of infinitesimal material line elements before and after deformation. Then, the deformation is considered of three non-coplanar infinitesimal material line elements lying along vectors M,N,P emanating from a particle at X in a body. An identity is derived relating the stretches along M,N,P and the angles between the three pairs of infinitesimal material line elements before and after deformation. The identity is factored leading to easy interpretation. The special case of infinitesimal strain is considered.      

On the Buckling of Axially Compressed Thin Cylindrical Shells

ABSTRACT

A simple general method for the evaluation of the effect of shape imperfections on the buckling of thin shells is briefly presented. This method is applied to the axially compressed thin cylindrical shell resulting in an efficient numerical procedure for the computation of its buckling strength. The procedure is applicable to any sufficiently smooth imperfection pattern and has given results in good agreement with the available experimental data.     

Global existence and blow-up phenomena of classical solutions for the system of compressible adiabatic flow through porous media

By means of maximum principle for nonlinear hyperbolic systems, the results given by HSIAO Ling and D. Serre was improved for Cauchy problem of compressible adiabatic flow through porous media, and a complete result on the global existence and the blowup phenomena of classical solutions of these systems. These results show that the dissipation is strong enough to preserve the smoothness of ‘ small ‘ solution.     

On Anisotropic Elastic Materials for which Young''s Modulus E ( n ) is Independent of n or the Shear Modulus G ( n , m ) is Independent of n and m

It is shown that, among anisotropic elastic materials, only certain orthotropic and hexagonal materials can have Young modulus E(n) independent of the direction n or the shear modulus G(n,m) independent of n and m. Thus the direction surface for E(n) can be a sphere for certain orthotropic and hexagonal materials. The structure of the elastic compliance for these materials is presented, and condition for identifying if the material is orthotropic or hexagonal is given. We also study the case in which n of E(n) and n, m of G(n,m) are restricted to a plane. When E(n) is a constant on a plane so are G(n,m) and Poisson's ratio ν(n,m). The converse, however, does not necessarily hold. A plane on which E(n) is a constant can exist for all anisotropic elastic materials. In particular, existence of such a plane is assured for trigonal, hexagonal and cubic materials. In fact there are four such planes for a cubic material. For these materials, not only E(n) is a constant, two other Young's moduli, the three shear moduli and the six Poisson's ratio on the plane are also constant.     

Dynamic Tensile Response of a Microwave Damaged Granitic Rock

Background

Understanding the dynamic tensile response of microwave damaged rock is of great significance to promote the development of microwave-assisted hard rock breakage technology. However, most of the current research on this issue is limited to static loading conditions, which is inconsistent with the dynamic stress circumstances encountered in real rock-breaking operations.

Objective

The objective of this work is to investigate the effects of microwave irradiation on the dynamic tensile strength, full-field displacement distribution and average fracture energy of a granitic rock.

Methods

The split Hopkinson pressure bar (SHPB) system combined with digital image correlation (DIC) technique is adopted to conduct the experiments. The overload phenomenon, which refers to the strength over-estimation phenomenon in the Brazilian test, is validated using the conventional strain gauge method. Based on the DIC analysis, a new approach for calculating the average fracture energy is proposed.

Results

Experimental results show that both the apparent and true tensile strengths increase with the loading rate while decreasing with the increase of the irradiation duration; and the true tensile strength after overload correction is lower than the apparent strength. Besides, the overload ratio and fracture energy also show the loading rate and irradiation duration dependency.

Conclusions

Our findings prove clearly that microwave irradiation significantly weakens the dynamic tensile properties of granitic rock.

     

ON THE WELL POSEDNESS OF INITIAL VALUE PROBLEM FOR EULER EQUATIONS OF INCOMPRESSIBLE INVISCID FLUID(Ⅱ)

The solvability of the Euler equations about incompressible inviscid fluid based on the stratification theory is discussed. And the conditions for the existence of formal solutions and the methods are presented for calculating all kinds of ill-posed initial value problems. Two examples are given as the evidences that the initial problems at the hyper surface does not exist any unique solution. Foundation item: the National Natural Science Foundation of China (19971054) Biography: Shen Zhen (1977−)     

Scale effects on strength of geomaterials, case study: Coal

Scale effects on the strength of coal are studied using a discrete element model. The key point of the model is its capability to discriminate between the “strictly sample size” effect and the “Discrete Fracture Network (DFN) density” effect on the mechanical response. Simulations of true triaxial compression tests are carried out to identify their respective roles. The possible bias due to the discretization size distribution of the discrete element model is investigated in detail by considering low-resolution configurations. The model is shown to be capable of quantitatively reproducing the dependency of the maximum strength on the size of the sample. This relationship mainly relies on the DFN density. For all given sizes, as long as the DFN density remains constant with a uniform distribution or if discontinuities are absent in the considered medium, the maximum strength of the material remains constant.     

The Potential Scope of the Ultrasonic Surface Reflection Method Towards Mechanical Characterisation of Isotropic Materials. Part 2. Experimental Results

Background

This paper is Part 2 of a study on the scope of the ultrasonic Surface Reflection Method (SRM). Part 1 deals with the theoretical conditions for a satisfactory usage of this method.

Objective

This second part validates the practical feasibility and reliability of the SRM method by comparison with the conventional Transmission Method (TM) in cases where the latter is applicable.

Methods

Two experimental devices (one for SRM and one for TM) are developed and measurements of shear and bulk moduli are carried out at ultrasonic frequency (610 kHz) and at room temperature.

Results

The experimental conditions in terms of sample geometry, pulse characteristics and interfacial transmission required to obtain a given accuracy on the measurement are stated. The SRM is then validated against other experimental methods and is used to determine the shear modulus of a carbon black filled neoprene at ambient temperature (T?=?21 °C) and ultrasonic frequency.

Conclusions

The benefit brought by this method is well demonstrated: a unique measurement allows the determination of all the moduli of a highly damping isotropic material (carbon black filled neoprene) not achievable by other methods.