An innovative multi-component variate that reveals hierarchy and evolution of structural damage in a solid: application to acrylic bone cement.

A major limitation of solid mechanics is the inability to take into account the influence of hierarchy and evolution of the inherent microscopic structure on evaluating the performance of materials. Irreversible damage and fracture in solids, studied commonly as cracks, flaws, and conventional material properties, are by no means descriptive of the subsequent responses of the microstructures to the applied load. In this work, we addressed this limitation through the use of a novel multi-component variate. The essence of this variate is that it allows the presentation of the random damage in the amplitude spectrum, probability space, and probabilistic entropy. Its uniqueness is that it reveals the evolution and hierarchy of random damage in multi- and trans-scales, and, in addition, it includes the correlations among the various damage features. To better understand the evolution and hierarchy of random damage, we conducted a series of experiments designed to test three variants of a poly (methyl methacrylate) (PMMA) bone cement, distinguished by the methods used to sterilize the cement powder. While analysis of results from conventional tension tests and scanning electron microscopy failed to pinpoint differences among these cement variants, our multi-component variate allowed quantification of the multi- and trans-scale random damage events that occurred in the loading process. We tested the statistical significance of damage states to differentiate the responses at the various loading stages and compared the damage states among the groups. We also interpreted the hierarchical and evolutional damage in terms of the probabilistic entropy (s), the applied stress (σ), and the trajectory of damage state. We found that the cement powder sterilization method has a strong influence on the evolution of damage states in the cured cement specimens when subjected to stress in controlled mechanical tests. We have shown that in PMMA bone cements, our damage state variate has the unique ability to quantify and discern the history and evolution of microstructural damage.

Probabilistic characteristics of random damage events and their quantification in acrylic bone cement.

The failure of brittle and quasi-brittle polymers can be attributed to a multitude of random microscopic damage modes, such as fibril breakage, crazing, and microfracture. As the load increases, new damage modes appear, and existing ones can transition into others. In the example polymer used in this study--a commercially available acrylic bone cement--these modes, as revealed by scanning electron microscopy of fracture surfaces, include nucleation of voids, cracking, and local detachment of the beads from the matrix. Here, we made acoustic measurements of the randomly generated microscopic events (RGME) that occurred in the material under pure tension and under three-point bending, and characterized the severity of the damage by the entropy (s) of the probability distribution of the observed acoustic signal amplitudes. We correlated s with the applied stress (σ) by establishing an empirical s-σ relationship, which quantifies the activities of RGME under Mode I stress. It reveals the state of random damage modes: when ds/dσ > 0, the number of damage modes present increases with increasing stress, whereas it decreases when ds/dσ < 0. When ds/dσ ≈ 0, no new random damage modes occur. In the s-σ curve, there exists a transition zone, with the stress at the "knee point" in this zone (center of the zone) corresponding to ~30 and ~35% of the cement's tensile and bending strengths, respectively. This finding explains the effects of RGME on material fatigue performance and may be used to approximate fatigue limit.

Random damage and characteristics of debris particles are two important and yet ignored factors in the mechanical integrity of the stem-cement interface of a total hip replacement: influence of the surface finish of the metal stem.

The importance of the conditions at the stem-cement interface in cemented total joint replacements (THRs) with regard to the in vivo longevity of the implant is well recognized. In the present study, we used a simplified model of one part of a cemented THR (alloy rectangular beam bonded to rectangular cement plate) to study the influence of surface finish of the alloy beam (stem) on two measures of the evolution of random damage at the alloy beam-cement plate interface (stem-cement interface), under quasi-static direct shear load. Three surface finishes of the beams were used: satin-finish, grit-blasted, and plasma-sprayed. The random damage events were monitored from the emitted acoustic signals, with the two measures computed from these signals being the intensity of random damage events (IRDE) and the mean damage event energy (MDEE). Large number of random damage events (higher values of IRDE and low value of MDEE) occurred with grit blasted specimens, suggesting a high probability for the generation of debris particles at the interface. These findings, in conjunction with details on the size and shape of the debris particles, obtained using scanning electron microscopy, lead to the suggestion that satin-finish stems are desirable for use in cemented THRs.