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.

Analysis of the geometrical influence of ring-opening samples on arterial circumferential residual stress reconstruction.

This work consists of analyzing the impact of geometrical features (thickness and curvature) on the estimation of circumferential residual stresses in arteries. For this purpose, a specific sample of lamb abdominal artery is chosen for analysis and, through computational tools based on Python libraries, the stress-free geometry is captured after the ring opening test. Numerical simulations are then used to reconstruct the sample in order to estimate the circumferential residual stresses. Then, four stress-free geometry models are analyzed: an ideal geometry, i.e., constant curvature and thickness; a constant curvature and variable thickness geometry; a variable curvature and constant thickness geometry; and a variable curvature and thickness geometry. The numerical results show that models perform well from a geometric point of view, where the most different feature was the closed outer perimeter that differs about 14% from the closed real sample. As far as residual stress is concerned, differences up to 198% were found in more realistic models taking a constant curvature and thickness model as reference. Thus, the analysis of a realistic geometry with highly variable curvature and thickness can introduce, compared to an idealized geometry, significant differences in the estimation of residual stresses. This could indicate that the characterization of arterial residual stresses is not sufficient when considering only the opening angle and, therefore, it is also necessary to incorporate more geometrical variables.

Analysis of the Stress Field in Photoelasticity Used to Evaluate the Residual Stresses of a Plastic Injection-Molded Part.

The degree of quality of thermoplastic injection-molded parts can be established based on their weight, appearance, and defects. However, the conditions of the injection process may induce effects on the mechanical performance of the injected parts, and the residual stresses can cause cracks or early failures when an external load or force is applied. To evaluate these mechanical behaviors, different experimental techniques have been reported in the literature, where digital photoelasticity has stood out both for being a non-contact technique and for achieving quantitative results through sophisticated computational algorithms. Against this background, our proposal consists of analyzing the overall residual stress distribution of parts injected under different molding conditions by using digital photoelasticity. In this case, the specimens are subjected to bending strength tests to identify possible effects of the injection process conditions. The findings show that, at mold temperatures of 80 °C, flow-induced residual stresses increase with packing pressure. However, these internal stress levels do not affect the external load applied by the mechanical bending test, while the mass injected at higher levels of packing pressure helps to increase the bending strength of the injected part. At lower mold temperatures (50 °C), the mechanical strength of the injected part is slightly reduced, possibly due to a lower effect of the packing pressure.

Study of the Evolution of the Plastic Zone and Residual Stress in a Notched T-6061 Aluminum Sample.

Using experimental measurements and numerical computations, this paper focuses on studying the evolution of the plastic zone and how the residual stresses change in a notched T-6061 aluminum sample. Before the crack initiation, digital image measurements were taken to visualize the evolution of the plastic zone. After the sample was fractured, the material microstructure and the residual stresses around the cracked zone were characterized through optical microscopy and X-ray diffractometry. This article describes in detail how the plastic zone evolved around the notch before the crack initiation and shows the close agreement between experimental and numerical data during the load increment. The surface residual stress values around the tip of the notched sample were also measured and computed to give a better understanding of the affected region during the fracture process.

Residual stresses explaining clinical fractures of bilayer zirconia and lithium disilicate crowns: A VFEM study.

OBJECTIVE: To understand the stress development in porcelain-veneered zirconia (PVZ) and porcelain-veneered lithium disilicate (PVLD) crowns with different veneer/core thickness ratios and cooling rates. To provide design guidelines for better performing bilayer restorations with the aid of Viscoelastic Finite Element Method (VFEM). METHODS: The VFEM was validated by comparing the predicted residual stresses with experimental measurements. Then, the model was used to predict transient and residual stresses in the two bilayer systems. Models with two different veneer/core thickness ratios were prepared (2:1 and 1:1) and two cooling protocols were simulated (Fast: ∼300 °C/min, Slow: ∼30 °C/min) using the heat transfer module, followed by stress analysis in ABAQUS. The physical properties of zirconia, lithium disilicate, and the porcelains used for the simulations were determined as a function of temperature. RESULTS: PVLD showed lower residual stresses than PVZ. The maximum tensile stresses in PVZ were observed in the cusp area, whereas those in PVLD were located in the central fossa. The 1:1 thickness ratio decreased stresses in both layers of PVZ. Slow cooling slightly decreased residual stresses in both systems. However, the cooling rate effect was more evident in transient stresses. SIGNIFICANCE: Slow cooling is preferable for both systems. A thinner porcelain layer over zirconia lowers stresses throughout the restoration. The different stress distributions between PVZ and PVLD may affect their failure modes. Smaller mismatches in modulus, CTE, and specific heat between the constituents, and the use of low Tg porcelains can effectively reduce the deleterious transient and residual tensile stresses in bilayer restorations.

Why a zero CTE mismatch may be better for veneered Y-TZP structures.

OBJECTIVE: Compare residual stress distribution of bilayered structures with a mismatch between the coefficient of thermal expansion (CTE) of framework and veneering ceramic. A positive mismatch, which is recommended for metal-ceramic dental crowns, was hypothesized to contribute to a greater chipping frequency in veneered Y-TZP structures. In addition, the multidirectional nature of residual stresses in bars and crowns is presented to explore some apparent contradictions among different studies. METHODS: Planar bar and crown-shaped bilayered specimens with 0.7 mm framework thickness and 1.5 mm porcelain veneer thickness were investigated using finite element elastic analysis. Eight CTE mismatch conditions were simulated, representing two framework materials (zirconia and metal) and six veneering porcelains (distinguished by CTE values). Besides metal-ceramic and zirconia-ceramic combinations indicated by the manufacturer, models presenting similar mismatch values (1 ppm/°C) with different framework materials (metal or zirconia) and zirconia-based models with metal-compatible porcelain veneers were also tested. A slow cooling protocol from 600 °C to room temperature was simulated. The distributions of residual maximum and minimum principal stresses, as well as stress components parallel to the long axis of the specimens, were analysed. RESULTS: Planar and crown specimens generated different residual stress distributions. When manufacturer recommended combinations were analysed, residual stresses obtained for zirconia models were significantly higher than those for metal-based models. When zirconia frameworks were combined with metal-compatible porcelains, the residual stress values were even higher. Residual stresses were not different between metal-based and zirconia-based models if the CTE mismatch was similar. SIGNIFICANCE: Some conclusions obtained with planar specimens cannot be extrapolated to clinical situations because specimen shape strongly influences residual stress patterns. Since positive mismatch generates compressive hoop stresses and tensile radial stresses and since zirconia-based crowns tend to be more vulnerable to chipping, a tensile stress-free state generated with a zero CTE mismatch could be advantageous.

Leucite and cooling rate effect on porcelain-zirconia mechanical behavior.

OBJECTIVE: This study investigated the influence of the cooling protocol on the mechanical behavior of Y-TZP veneered with porcelain with different compositions. The tested hypotheses were: (1) Y-TZP infrastructures veneered with porcelain containing leucite in its composition presents higher flexural strength (σ) and reliability (m), and (2) slow cooling protocol results in greater σ and m. METHODS: A total of 120 bilayer porcelain-Y-TZP bar-shaped specimens were prepared with the dimensions of 1.8mm (0.8mm Y-TZP±1.0mm porcelain)×4.0mm×16.0mm. Specimens were divided into four groups (n=30) according to the porcelain composition (containing or not leucite) and cooling protocol. Fast cooling was performed by opening the furnace chamber at sintering temperature. For the slow cooling, the chamber was maintained closed until it reached the room temperature. Specimens were tested in three-point bending with the porcelain surface under tension using a universal testing machine, in 37°C water, at 0.5mm/min crosshead speed. Data were analyzed by two-way ANOVA, Tukey post-hoc test (α=0.05) and Weibull. RESULTS: Y-TZP veneered with porcelains with different microstructural composition presented similar σ and m values (p=0.718). The cooling protocol had no influence on the σ and m values of the experimental groups (p=0.718). Cracking represented 95% of failures, whereas the initial flaw propagated from the porcelain surface towards the interface. SIGNIFICANCE: Y-TZP veneered with porcelain containing or not leucite present similar mechanical behavior and, at 1-mm thickness, is not sensitive to the cooling protocol.

Residual stress profiles in veneering ceramic on Y-TZP, alumina and ZTA frameworks: measurement by hole-drilling.

OBJECTIVES: The residual stress profile developed within the veneering ceramic during the manufacturing process is an important predicting factor in chipping failures, which constitute a well-known problem with yttria-tetragonal-zirconia polycrystal (Y-TZP) based restorations. The objectives of this study are to measure and to compare the residual stress profile in the veneering ceramic layered on three different polycrystalline ceramic framework materials: Y-TZP, alumina polycrystal (AL) and zirconia toughened alumina (ZTA). METHODS: The stress profile was measured with the hole-drilling method in bilayered disk samples of 19 mm diameter with a 0.7 mm thick Y-TZP, AL or ZTA framework and a 1.5mm thick layer of the corresponding veneering ceramic. RESULTS: The AL samples exhibited increasing compressive stresses with depth, while compressive stresses switching into interior tensile stresses were measured in Y-TZP samples. ZTA samples exhibited compressive stress at the ceramic surface, decreasing with depth up to 0.6mm from the surface, and then becoming compressive again near the framework. SIGNIFICANCE: Y-TZP samples exhibited a less favorable stress profile than those of AL and ZTA samples. Results support the hypothesis of the occurrence of structural changes within the Y-TZP surface in contact with the veneering ceramic to explain the presence of tensile stresses. Even if the presence of Y-TZP in the alumina matrix seems to negatively affect the residual stress profiles in ZTA samples in comparison with AL samples, the registered profiles remain positive in terms of veneer fracture resistance.