Cumulative damage model

D.H. Allen et al A cumulative damage model for continuous fiber composite laminates with matrix cracking and interply delaminations. ASTM Sp. Tech. Pub. 972, 57-80 (1988)... 

Hwang, W. and K. Han (1986). Cumulative damage models and multi-stress fatigue life prediction. Composite Materials 20, 125-153. 

Zhang et al. 2007) consider a bivariate policy in which the system is replaced when its working age reaches T or the accumulated number of failures is A and determine the optimal replacement policy. (Nakagawa 2005) provides a thorough review of maintenance policies. (Nakagawa 2007) studies optimum policies for cumulative damage models. 

The theory of stochastic processes and its apph-cations to reliability analysis have been discussed in several monographs (Aven and Jensen 1999, Tijms 2003). The cumulative damage models are popularly applied to the optimization of maintenance policies using the condition or age based criteria. Nakagawa (1976) formulated a preventive maintenance pohcy. 

Springer series in reliability engineering. London, U.K. Nakagawa, T., 1976. On a replacement problem of a cumulative damage model. Operational Research Quarterly 27(4), 895-900. 

Nakagawa, T. and Kijima, M., 1989. Replacement policies for a cumulative damage model with minimal repair at failure. IEEE Transactions on Reliability, 38(5),581 584. Nakagawa, T. and Yasui, K., 1991. Periodic replacement models with threshold levels. IEEE Transactions on Reliability, 40(3),395-397. 

McKenna and Penn (29) developed a model for predicting the fatigue life of polymers and applied it to an amorphous glass, PMMA, and polyethylene. The model is characterized within the framework of a cumulative damage model. They... 

Keywords Service-life prediction Real-world validation Degradation pathways Degradation-rate model Accelerated life testing Cumulative damage model... 

Degradation-rate model Accelerated life testing Cumulative damage model... 

Martin, J.W., Nguyen, T., Byrd, E., Dickens, B., Embree, N. Relating laboratory and ourdoor exposure of acrylie eoatings. I. Cumulative damage model and laboratory exposure apparatus. Polym. Degrad. Stab. 75, 193-210 (2002)... 

The numerical sidesway collapse prediction depends on the model capabilities. Historically, the first nonlinear numerical models did not include deteriorating characteristics, and damage indexes were developed to predict collapse based on maximum displacements and/or dissipated energy. The most widespread cumulative damage model was the Park-Ang model (Park and Ang 1985), which was developed specifically for reinforced concrete components. The damage measure (DM) consisted of a linear combination of displacement and energy demands ... 

Non-linear constitutive equations are developed for highly filled polymeric materials. These materials typically exhibit an irreversible stress softening called the "Mullins Effect." The development stems from attempting to mathematically model the failing microstructure of these composite materials in terms of a linear cumulative damage model. It is demonstrated that p order Lebesgue norms of the deformation history can be used to describe the state of damage in these materials and can also be used in the constitutive equations to characterize their time dependent response to strain distrubances. This method of analysis produces time dependent constitutive equations, yet they need not contain any internal viscosity contributions. This theory is applied to experimental data and shown to yield accurate stress predictions for a variety of strain inputs. Included in the development are analysis methods for proportional stress boundary valued problems for special cases of the non-linear constitutive equation. 

---