Coupled processes of deformation and long-term damage of fibrous materials with the microdurability of the matrix described by an exponential power function

2011

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A theory of long-term damage of physically nonlinear homogeneous materials is proposed. Damage 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 Huber-Mises criterion, and assumed to be a random function of coordinates. An equation of damage (porosity) balance in a physically nonlinear material at an arbitrary time is formulated. Algorithms of calculating the time dependence of microdamage and macrostresses are developed and the corresponding curves are plotted. The effect of the nonlinearity of the material on its macrodeformation and damage is analyzed Introduction. A possible cause of failure of materials and structural members under loading is the occurrence and development of dispersed microdamages, which commonly lead to the formation of main cracks. Physically, the damage of a material may be considered as dispersed defects such as microcracks, microvoids, or destroyed microvolumes. They reduce the effective or bearing portion of the material that resists loads.Experimental data on and experience of using structural members and structures 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 [7,9,10]. It employs the mechanics of microinhomogeneous bodies of structure stochastic 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 statistically inhomogeneous, 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 constant tensile stress, 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, which depends on the difference between the applied stress and the ultimate microstrength. The theory of long-term damage of homogeneous and fibrous materials was developed in [8,11,12] based on models and methods of the mechanics of stochastically inhomogeneous materials.Under high loads, many materials exhibit physical nonlinearity. This type of nonlinearity is typical of metals and polymeric materials at high temperatures. Therefore, it is important to generalize the theory of long-term damage of homogeneous materials [8] based on models and methods of the mechanics of stochastically inhomogeneous materi...

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Theory of long-term microdamage of physically nonlinear homogeneous materials

2011

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“…Therefore, it is important to generalize the theory of long-term damage of fibrous composite materials [11,12] based on models and methods of the mechanics of stochastically inhomogeneous materials to physically nonlinear particulate materials. The damage of the components of a particulate composite is modeled by dispersed microvolumes destroyed to become randomly arranged micropores.…”

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confidence: 99%

Deformation and long-term damage of physically nonlinear particulate composites

2011

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The theory of long-term damage is generalized to particulate composite materials with physically nonlinear components. The damage of the components is modeled by randomly dispersed micropores. The damage criterion for a microvolume is characterized by its stress-rupture strength. It is determined by the dependence of the time to brittle failure on the difference between the equivalent stress and its limit, which is the ultimate strength, according to the Huber-Mises criterion, and assumed to be a random function of coordinates. An equation of damage (porosity) balance in the components at an arbitrary time is formulated. Algorithms of calculating the time dependence of are developed. The effect on the nonlinearity of the matrix on the damage and macrodeformation curves is examined Introduction. High loads cause dispersed microdamages in materials and structural members, which commonly lead to the formation of main cracks. 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.Experimental data on and observation of the behavior of structural members and structures 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). The structural theory of short-term microdamage of homogeneous and composite materials [7,9,10] employs the mechanics of microinhomogeneous bodies of stochastic structure and models dispersed microdamages by quasispherical micropores [5]. Long-term damage is accumulation of dispersed microdamages such as micropores and microcracks. The strength of a material is micro-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. Under constant tensile stress, 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, which depends on the difference between the applied stress and the ultimate microstrength. The theory of long-term damage of homogeneous and fibrous materials was developed in [8, 11, 12] based on models and methods of the mechanics of stochastically inhomogeneous materials.The stress-strain behavior of many materials such as metals and polymers becomes nonlinear at high temperatures. Therefore, it is important to generalize the theory of long-term damage of fibrous composite materials [11,12] based on models and methods of the mechanics of stochastically inhomogeneous materials to physically nonlinear particulate materials. The damage of the components of a particulate composite is modeled by dispersed microvolumes destroyed to become randomly arranged micropores. The failure criterion for a single...

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

2011

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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...