Mathematical model for the plastic flow and ductile fracture of polycrystalline solids.

It is mathematically shown that ductile fracture after finite plastic strain is a necessary consequence of the polycrystalline nature of the materials. A closed-form equation for the plastic strain to fracture of a fine-grained polycrystal with no voids is derived. The mathematical model for the plastic deformation is grounded on the physical hypothesis that adjacent grains slide with a relative velocity proportional to the local shear stress resolved in the plane of the shared grain boundary, when exceeds a finite threshold. Hence plastic flow is governed predominantly by the in-plane shear forces making grain boundaries to slide, and the induced local forces responsible for the continuous grain reshaping are much weaker. The process is shown to produce a monotonic hydrostatic pressure variation with strain that precludes a stationary flow. The hydrostatic pressure dependence on strain has two solutions. One of them leads to superplasticity, the other one is shown to diverge logarithmically at a finite fracture strain and then represents ductile behaviour. Emphasis is done in the mathematical aspects of the deformation of the polycrystal up to the initiation of fracture. Although theoretical predictions agree well with mechanical tests of commercial alloys, technical issues like the effects of the presence and evolution of porosity and other imperfections, or how fracture evolves after initiation are left for a more specific communication.

Impact and flexural strength, and fracture morphology of acrylic resins with impact modifiers.

OBJECTIVES: This study evaluated the impact and flexural strength and analyzed the fracture behavior of acrylic resins. METHODS: Eighteen rectangular specimens were fabricated of Lucitone 550, QC 20 (both unreinforced acrylic resins), Impact 1500 (extra strength impact), Impact 2000 (high impact) according to the manufacturers' instructions. The impact strength was evaluated in notched specimens (50x6x4mm) and flexural strength in unotched (64x10x3.3mm), using three-point bending test, as well as, stress at yield, Young modulus and displacement at yield. Fragments from mechanical tests were observed by SEM. Data from impact strength, stress at yield and displacement at yield were analyzed by 1-way ANOVA and Tukey test (alpha=0.05). Young modulus values were analyzed by One-way ANOVA and Dunnett T3 multiple comparisons test (alpha=0.05). RESULTS: Mean values of impact strength and stress at yield values were higher (P<.005) for Impact 2000 while Young modulus was higher (P<.05) for Lucitone 550; Impact 1500 and Impact 2000 showed significant values (P<.05) in the displacement at yield. Impact fractures of the all acrylic resins were brittle. Bending fractures of Lucitone 550 and Impact 2000 were brittle, QC 20 fractures were ductile and Impact 1500 showed brittle (75%) and ductile (25%) fractures. CONCLUSION: Within the limitations of this study, the Impact 2000 showed improved mechanical properties with high capacity of stress absorption and energy dissipation before the fracture.