Novel Ring Compression Test Method to Determine the Stress-Strain Relations and Mechanical Properties of Metallic Materials

Although there are methods for testing the stress-strain relation and strength, which are the most fundamental and important properties of metallic materials, their application to small-volume materials and tube components is limited. In this study, based on energy density equivalence, a new dimensionless elastoplastic load-displacement model for compressed metal rings with isotropy and constitutive power law is proposed to describe the relations among the geometric dimensions, Hollomon law parameters, load, and displacement. Furthermore, a novel test method was developed to determine the elastic modulus, stress-strain relation, yield and tensile strength via ring compression test. The universality and accuracy of the method were verified within a wide range of imaginary materials using finite element analysis (FEA), and the results show that the stress-strain curves obtained by this method are consistent with those inputted in the FEA program. Additionally, a series of ring compression tests were performed for seven metallic materials. It was found that the stress-strain curves and mechanical properties predicted by the method agreed with the uniaxial tensile results. With its low material consumption, the ring compression test has the potential to be as an alternative to traditional tensile test when direct tension method is limited.

An unified formulation of strong non-local elasticity with fractional order calculus

The research of a formulation to model non-local interactions in the mechanical behavior of matter is currently an open problem. In this context, a strong non-local formulation based on fractional calculus is provided in this paper. This formulation is derived from an analogy with long-memory viscoelastic models. Specifically, the same kind of power-law time-dependent kernel used in Boltzmann integral of viscoelastic stress-strain relation is used as kernel in the Fredholm non-local relation. This non-local formulation leads to stress-strain relation based on the space Riesz integral and derivative of fractional order. For unbounded domain, proposed model can be defined in stress- and in strain-driven formulation and in both cases the stress–strain relation represent a strong non-local model. Also, the proposed strain driven and stress driven formulations defined in terms of Riesz operators are proved to be fully consistent each another. Moreover, the proposed model posses a mechanical meaning and for unbounded non-local rod is described and discussed in detail.

Cumulative Shear Damage Mechanism to Short Fiber Type C/SiC

A cumulative damage mechanism for short fiber type C/SiC during shear loading–unloading testing was examined and quantified using Iosipescu specimens parallel in the in-plane and through-thickness plane, and by using modified fracture and damage mechanics theory referring to measured damage characteristics (crack length, number and angle). A nonlinear stress–strain relation was found for both specimens. Decrease in the apparent modulus was confirmed with increased peak stress, although permanent strain increased. Inelastic strain of the decomposed tensile direction derived from shear stress was greater than that of the compressive one. Cracks propagated perpendicularly to the tensile direction, intruding on the boundary of the transverse fibers and connecting to other cracks. The theoretical damage mechanics model succeeded to predict the stress–strain relation, proposing that the shear mechanical properties are predictable by measuring the damage characteristics.

Thermodynamic Foundation of Generalized Variational Principle

One open question remains regarding the theory of the generalized variational principle, that is, why the stress-strain relation still be derived from the generalized variational principle while the Lagrangian multiplier method is applied in vain? This study shows that the generalized variational principle can only be understood and implemented correctly within the framework of thermodynamics. As long as the functional has one of the combination $A(\epsilon_{ij})-\sigma_{ij}\epsilon_{ij}$ or $B(\sigma_{ij})-\sigma_{ij}\epsilon_{ij}$, its corresponding variational principle will produce the stress-strain relation without the need to introduce extra constraints by the Lagrangian multiplier method. It is proved herein that the Hu-Washizu functional $\Pi_{HW}[u_i,\epsilon_{ij},\sigma_{ij}]$ and Hu-Washizu variational principle comprise a real three-field functional.

Analytical stress-strain relation for soils

A new stress-strain relation capable of reproducing the entire stress-strain range of typical soil tests is presented. The new relation involves a total of five parameters, four of which can be inferred directly from typical test data. The fifth parameter is a fitting parameter with a relatively narrow range. The capabilities of the new relation is demonstrated by the application to various clay and sand data sets.

Novel Ring Compression Test Method to Determine the Stress-strain Relations and Mechanical Preperties of Metallic Materials

Although there are methods for testing the stress–strain relation and strength, which are the most fundamental and important properties of metallic materials, their application to small size specimens is limited. In this study, a new dimensionless elastoplastic load–displacement (EPLD-Ring) model for compressed metal rings with isotropy and constitutive power law is proposed to describe the relation between the geometric dimensions, Hollomon law parameters, load, and displacement based on energy density equivalence. Furthermore, a novel test method for the rings is developed to obtain the elastic modulus, stress–strain relation, yield strength, and tensile strength. The universality and accuracy of the model are verified within a wide range of imaginary materials via finite element analysis (FEA), and the results show that the stress–strain relations obtained with the model are more consistent with those inputted in the FEA software. Additionally, for seven metallic materials, a series of ring compression tests with various dimensions were performed. It was found that the stress–strain relations and mechanical properties predicted by the model are in agreement with the normal tensile test results. It is believed that the new method is reliable and effective for testing the mechanical properties of small size materials and tube components.