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.