Coupled processes of deformation and long-term damage of fibrous materials under thermal loading

Abstract

A theory of long-term damage of fibrous composites under thermal loading is set up. The damage of the matrix is modeled by randomly dispersed micropores. The failure criterion for a microvolume is characterized by its stress-rupture strength. It is determined by the dependence of the time to brittle fracture on the difference between the equivalent stress and its limit, which is the ultimate strength, according to the Schleicher-Nadai failure criterion, and assumed to be a random function of coordinates. An equation of damage (porosity) balance in the matrix at an arbitrary time is formulated taking into account the thermal component. Algorithms of calculating the time dependence of microdamage and macrostresses are developed. Corresponding curves are plotted. The effect of temperature on the deformation and microdamage of the material is studied Keywords: fibrous composite, stochastic structure, thermal effect, long-term damage, porosity, effective characteristics, porosity balance equationIntroduction. Materials and structural members may collapse under high loads. Failure is commonly preceded by occurrence and development of dispersed microdamages.Microdamages are chaotically dispersed damaged microvolumes that have completely or partially lost their load-carrying capacity. They reduce the effective or bearing portion of the material that resists loads. During deformation, microdamages may occur when microstresses reach local limits of strength.Experiments and observations suggest that damage can be either short-term (occurring instantaneously after the application of stresses or strains) or long-term (building up with time after the application of load). A structural theory of short-term microdamage of homogeneous and composite materials was proposed in [8,9,11]. It employs the mechanics of microinhomogeneous bodies of stochastic structure and models dispersed microdamages by quasispherical micropores [5]. Long-term damage is usually considered as accumulation of dispersed microdamages such as micropores and microcracks. At the microscopic level, the strength of a material is nonuniform, i.e., the ultimate strength and stress-rupture curves for a microvolume are random functions of coordinates with certain distribution density or cumulative distribution. When a macrospecimen is subject to a constant tensile load, some microvolumes whose ultimate strength is less than the applied stress are damaged, i.e., microcracks or micropores form in their place. Microvolumes where the stress is less than, yet close to the ultimate strength are damaged after a lapse of time that depends on the difference between the stress and the ultimate microstrength.The theory of long-term damage of homogeneous and fibrous materials was developed in [10, 12, 13] based on models and methods of the mechanics of stochastically inhomogeneous materials.In the present paper, we will study the effect of thermal loads on the deformation and long-term damage of fibrous composite materials with microdamaged matrix. The structural theory of long...

Deformation and damage of linear elastic homogeneous and composite materials (review)

“…The macrostress-macrostrain relationship and the porosity balance equations for a composite material with porous components describe the coupled and interacting processes of deformation and long-term damage, which cause the macrostrains to increase at given time-dependent macrostresses and the macrostresses to decrease at given time-dependent macrostrains. The effect of temperature on the long-term damage and deformation of composites is taken into account [88][89][90][91]. An iteration method is used to develop algorithms for calculating the microdamage and macrostresses or microstrains as functions of time and to plot the respective curves.…”