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Master of Science / Department of Mechanical and Nuclear Engineering / Kevin Lease / Over the past several years the crack tip opening angle (CTOA) has been identified as one of the key fracture parameters to characterize low constraint stable tearing and instability in structural metallic alloys. This document presents the results of experimental stable tearing characterizations. Characterization methods include optical microscopy and marker band measurements of crack front tunneling. Specific attention is given to the measurement methods used, and also the correlation between CTOA and Delta-5. The effect of tunneling and comparisons with computational results are discussed, and the effect of material and measurement method on CTOA is observed and a clear relationship is seen. Preliminary work on future studies into internal features and behavior is also presented.

A computer-based parametric study of the effect of reinforcement architectures on fracture response of aluminum compact-tension (CT) specimens was performed using the finite element code ABAQUS. A three-dimensional crack propagation procedure based on the crack tip opening angle (CTOA) was developed using Python. Eleven different reinforcement architectures consisting of rectangular and triangular cross-section reinforcements were evaluated. Reinforced specimens produced between 13 and 28 percent higher fracture load than achieved with the non-reinforced case. Reinforcements with blunt leading edges (rectangular reinforcements) exhibited superior performance relative to the triangular reinforcements with sharp leading edges. Relative to the rectangular reinforcements, the most important architectural feature was reinforcement thickness. At failure, the reinforcements carried between 58 and 85 percent of the load applied to the specimen, suggesting that there is considerable load transfer between the base material and the reinforcement. The amount of load transfer is linked to strains experienced by the reinforcement ahead of the crack tip. / Master of Science

The molecular stress function model with convective constraint release (MSF with CCR) constitutive model [M.H. Wagner, P. Rubio, H. Bastian, The molecular stress function model for polydisperse polymer melts with dissipative convective constraint release, J. Rheol. 45 (2001) 1387] is capable of fitting all viscometric data for IUPAC LDPE, with only two adjustable parameters (with difference found only on reported ¿steady-state¿ elongational viscosities). The full MSF with CCR model is implemented in a backwards particle-tracking implementation, using an adaptive method for the computation of relative stretch that reduces simulation time many-fold, with insignificant loss of accuracy. The model is shown to give improved results over earlier versions of the MSF (without CCR) when compared to well-known experimental data from White and Kondo [J.L. White, A. Kondo, Flow patterns in polyethylene and polystyrene melts during extrusion through a die entry region: measurement and interpretation, J. Non-Newtonian Fluid Mech. 3 (1977) 41]; but still to under-predict contraction flow opening angles. The discrepancy is traced to the interaction between the rotational dissipative function and the large stretch levels caused by the contraction flow. A modified combination of dissipative functions in the constraint release mechanism is proposed, which aims to reduce this interaction to allow greater strain hardening in a mixed flow. The modified constraint release mechanism is shown to fit viscometric rheological data equally well, but to give opening angles in the complex contraction flow that are much closer to the experimental data from White and Kondo. It is shown (we believe for the first time) that a constitutive model demonstrates an accurate fit to all planar elongational, uniaxial elongational and shear viscometric data, with a simultaneous agreement with this well-known experimental opening angle data. The sensitivity of results to inaccuracies caused by representing the components of the deformation gradient tensor to finite precision is examined; results are found to be insensitive to even large reductions in the precision used for the representation of components. It is shown that two models that give identical response in elongational flow, and a very similar fit to available shear data, give significantly different results in flows containing a mix of deformation modes. The implication for constitutive models is that evaluation against mixed deformation mode flow data is desirable in addition to evaluation against viscometric measurements.

The extracellular matrix (ECM) of the aorta is a complex meshwork of elastin, collagen, and glycosaminoglycans (GAG). It also modulates the mechanical properties of the aorta, which in turn dictate lethal ruptures such as those caused by aneurysm and dissection. Amongst other roles, aortic stiffness controls the aorta’s ability to expand and recoil, and residual stresses, which are those existing in the absence of load, affect the magnitude and distribution of the mechanical stresses throughout the aortic wall. Mechanical stresses can be predicted via complex computer models, powerful tools that can also provide insight regarding the risk of rupture, given that ruptures occur when the mechanical stresses exceed the strength of the aorta. While this dissertation is primarily focused on the effect of GAG on residual stresses, other ECM (collagen, elastin) and mechanical (stiffness) factors are considered to expand our understanding of the structure-mechanics relationship in the aorta. This is important because the ECM undergoes extensive remodelling during aging and disease, but it is also critically important, as mentioned, in the context of aortic rupture. We first explored the mechanical roles of GAG in a finite element model by studying both the transmural residual stresses and the opening angle (an indicator of circumferential residual stresses) in ascending (AS) aortic ring models. Both were shown to be modulated by the GAG content, gradient, and the nature of the transmural distribution. While a heterogeneous GAG distribution led to the development of residual stresses which could be released by a radial cut, this was not the case when a homogeneous distribution was prescribed. Because the GAG distributions used in the first study were based on assumptions, and to get an in vitro understanding of the ECM role in modulating residual stresses, biomechanical mechanisms were explored in thoracic aortas from 5- to 6-month-old pigs. In a second study, we generated new detailed data on the distributions of collagen, elastin and GAG, throughout the aortic wall in the AS, arch (AR), and descending thoracic (DT) regions, and established correlations between the ECM constituents and the opening angle. The strongest correlations were observed between the opening angle and the total collagen:GAG ratio as well as the total GAG content. In line with our first in silico work, this in vitro investigation revealed that the GAG content and gradient modulate circumferential residual stresses and suggested that the interaction between GAG and the ECM fibers also plays a role in regulating residual stresses. In a third study, we examined the extent of contribution of GAG to circumferential residual stresses and to the radial compressive stiffness of the aortic wall, as well as the underlying mechanism through which GAG contribute to the mechanical properties using enzymatic GAG depletion. GAG depletion was associated with a decrease in the opening angle, by approximately 25%, 32%, 42% in the AS, AR, and lower DT regions respectively, and an increase in the radial compressive stiffness of the AS aorta. Glycation was also associated with a decrease in the opening angle, in which GAG depletion also had a similar effect. A small loss of water content was detected after GAG depletion, and the AS region was also associated with a significant loss of compressive deformation in the inner layer of the aorta following GAG depletion, suggesting that GAG interact with ECM fibers in their effect on aortic mechanics. The garnered experimental geometrical data and intramural GAG distributions were finally used to simulate animal-specific aortic rings from the AS, AR, and DT regions. The opening angle response was evaluated in solid matrices assuming one layer, and two layers to capture the different mechanical behaviors of the intima-media and the adventitia. A Holmes-Mow constitutive relationship was used and material parameters were obtained by curve fitting experimental stress-strain curves obtained from biaxial tests. Numerical results were evaluated by comparing simulated and experimental opening angles, revealing a notable overall agreement between the two.

Yes / The molecular stress function model with convective constraint release (MSF with CCR) constitutive model [J. Rheol. 45 (2001), 1387] is capable of fitting all viscometric data for IUPAC LDPE, with only two adjustable parameters (with difference found only on reported ¿steady-state¿ elongational viscosities). The full MSF with CCR model is implemented in a backwards particle-tracking implementation, using an adaptive method for the computation of relative stretch that reduces simulation time many-fold, with insignificant loss of accuracy. The model is shown to give improved results over earlier versions of the MSF (without CCR) when compared to well-known experimental data from White and Kondo [J. non-Newt. Fluid Mech., 3 (1977), 41]; but still to under-predict contraction flow opening angles. The discrepancy is traced to the interaction between the rotational dissipative function and the large stretch levels caused by the contraction flow. A modified combination of dissipative functions in the constraint release mechanism is proposed, which aims to reduce this interaction to allow greater strain hardening in a mixed flow. The modified constraint release mechanism is shown to fit viscometric rheological data equally well, but to give opening angles in the complex contraction flow that are much closer to the experimental data from White and Kondo. It is shown (we believe for the first time) that a constitutive model demonstrates an accurate fit to all planar elongational, uniaxial elongational and shear viscometric data, with a simultaneous agreement with this well-known experimental opening angle data. The sensitivity of results to inaccuracies caused by representing the components of the deformation gradient tensor to finite precision is examined; results are found to be insensitive to even large reductions in the precision used for the representation of components. It is shown that two models that give identical response in elongational flow, and a very similar fit to available shear data, give significantly different results in flows containing a mix of deformation modes. The implication for constitutive models is that evaluation against mixed deformation mode flow data is desirable in addition to evaluation against viscometric measurements.

A two-parameter fracture criterion (TPFC) is used to correlate and predict failure loads on cracked configurations made of ductile materials. The current study was conducted to validate the use of the fracture criterion on more brittle materials, using elastic-plastic finite-element analyses with the critical crack-tip-opening angle (CTOA) failure criterion. Forman generated fracture data on middle-crack tension, M(T), specimens made of thin-sheet 7075-T6 aluminum alloy, which is a quasi-brittle material. The fracture data included a wide range of specimen widths (2w) ranging from 3 to 24 inches. A two-dimensional (2D) finite-element analysis code (ZIP2D) with a ''plane-strain core" option was used to model the fracture process. Fracture simulations were conducted on M(T), single-edge-crack tension, SE(T), and single-edge-crack bend, SE(B), specimens. The results supported the TPFC equation for net-section stresses less than the material proportional limit. However, some discrepancies were observed among the numerical results of the three specimen types. Thus, more research is needed to improve the transferability of the TPFC from the M(T) specimen to both the SE(T) and SE(B) specimens.

The Two-Parameter-Fracture-Criterion (TPFC) was validated using an elastic-plastic two-dimensional (2D) finite-element code, ZIP2D, with the plane-strain-core concept. Fracture simulations were performed on three crack configurations: (1) middle-crack-tension, M(T), (2) single-edge-crack-tension, SE(T), and (3) single-edge crack-bend, SE(B), specimens. They were made of 2014-T6 (TL) aluminum alloy. Fracture test data from Thomas Orange work (NASA) were only available on M(T) specimens (one-half width, w = 1.5 to 6 in.) and they were all tested at cryogenic (-320oF) temperature. All crack configurations were analysed over a very wide range of widths (w = 0.75 to 24 in.) and crack-length-to-width ratios ranged from 0.2 to 0.8. The TPFC was shown to fit the simulated fracture data fairly well (within 6.5%) for all crack configurations for net-section stresses less than the material proportional limit. For M(T) specimens, a simple approximation was shown to work well for net-section stresses greater than the proportional limit. Further study is needed for net-section stresses greater than the proportional limit for the SE(T) and SE(B) specimens.

Yes / The Molecular Stress Function (MSF) constitutive model with convective constraint release mechanism has been shown to accurately fit a large range of viscometric data, and also shown to give strong vortex growth in flows of LDPE through planar and axisymmetric contractions. This work compares simulation and experimental results for 3-D flows of Lupolen 1840H LDPE through a contraction slit; 3-D effects are introduced by using a slit with a low upstream aspect ratio of 5:3. Comparisons are made with vortex opening angles obtained from streak photography, and also with stress birefringence measurements. The comparisons are made with two versions of the convective constraint release (CCR) mechanism. The simulated vortex angles for one version of the CCR mechanism are found to approach what is seen experimentally. The best-fit value for the stress optical coefficient was found to vary between CCRs and to decrease with flow rate. This is partially explained by different centreline elongational rates with the two CCRs, which in turn is related to different opening angles. A 3-D simulation is compared to the corresponding 2-D simulation. It is shown that both velocity vectors and birefringence show only small changes to around 60% of the distance to the side wall.