Dynamic fracture of metals is a fascinating multiphysics-multiscale problem that often results in brittle and/or ductile fracture of structural components. Additionally, under high strain rates such as impact or blast loads, a failure phenomena known as shear banding may also occur, which is a common precursor to fracture. Both fracture and shear banding are instability processes leading to strong discontinuities and strain localization, respectively. Namely, shear bands are zones of highly localized plastic deformation, while brittle/ductile cracks are material discontinuities due to cleavage and/or void coalescence. Furthermore, while fracture events are mostly driven by triaxial tensile loading, shear bands are driven by shear heating caused by inelastic deformations and high temperature rise. In this work, fracture is modeled through a phase field formulation coupled to a set of equations that describe shear bands. While fracture is governed by a strong length scale that propagates at a fast time scale, shear bands are dominated by a weak length scale and propagate slower. These are two different failure modes with distinct spatial and temporal scales. This thesis is aimed at the development of analytical and numerical methods to determine the onset of both shear band localization and fracture. The main contribution of this thesis is the formulation of analytical criteria, based on the linear perturbation method, for the onset of fracture and shear band instabilities. We first propose a stability framework for shear bands that account for a non-constant Taylor Quinney coefficient. In addition, we apply the linear perturbation method to the phase field formulation of fracture to study the onset of unstable crack growth. The derivations lead to an analytical, energy based criterion for the phase field method in linear elastic and visco-plastic materials. The stability criterion not only recovers the critical stress value reported in the literature for simple elastic cases but also provides a criterion for visco-plastic materials with a general degradation function and fracture induced by cold-work. Finally, we analyze the physical stability of both failure modes and their interaction. The analysis provides insight into the dominant failure mode and can be used as a criterion for mesh refinement. Several numerical results with different geometries and a range of strain rate loadings demonstrate that the stability criterion predicts well the onset of failure instability in dynamic fracture applications. For the example problems considered, if a fracture instability precedes shear banding, a brittle-like failure mode is observed, while if a shear band instability is initiated significantly before fracture, a ductile-like failure mode is expected. In any case, fracture instability is stronger than a shear band instability and if initiated will dominate the response. Another contribution of this thesis is the development of numerical type stability methods based on the discretized model which can be employed within any finite element method. In this approach, a novel methodology to determine the onset of shear band localization is proposed, by casting the instability analysis as a generalized eigenvalue problem with a particular decomposition of the element Jacobian matrix. We show that this approach is attractive, as it is applicable to general rate dependent multidimensional cases and no special simplifying assumptions ought to be made. Furthermore, this technique is also applied to the fully coupled dynamic fracture problem and is shown to agree well with the analytical criteria. Finally, we propose an alternative for identifying the instability point following a generalized stability analysis concept. In this framework, a stability measure is obtained by computing the instantaneous growth rate of the vector tangent to the solution. Such an approach is more appropriate for non-orthogonal problems and is easier to generalize to difficult dynamic fracture problems.

Este trabalho, realizado em cooperação com a Gerdau Riograndense, tem por finalidade avaliar o comportamento do aço GG1013-M, um aço baixo teor de carbono microligado com vanádio e manganês, na laminação a quente no que tange a sua resistência à deformação, possibilitando assim a tomada de decisão em relação a modificações no processo. Foram realizados testes em simulador termomecânico Gleeble™ para determinação das temperaturas a serem usadas no teste prático no laminador, onde testou-se lotes que cobrissem toda a amplitude da faixa de composição química da qualidade do aço em estudo. No teste prático no laminador, foram retiradas amostras para os ensaios mecânicos, onde identificou-se, por intermédio do tratamento de dados em software estatístico, a influência da variação dentro da faixa da composição química sobre os limites de escoamento e resistência. Como resultado, conseguiu-se determinar a faixa de temperatura mais provável, onde a resistência a deformação a quente é menor, minimizando ou eliminando as conseqüências da redução de ductilidade a quente por conta do endurecimento da matriz por precipitação dos elementos de liga em forma de compostos. / This work was conducted in cooperation with Gerdau Riograndense aiming at the evaluation of the hot rolling behavior of a low carbon steel microalloyed with manganese and vanadium (internally GG1013-M steel).The deformation resistance was evaluated, allowing for the decision in relation to changes in the process. A thermomechanical simulator GleebleTM was used to determine the temperatures to be used in practical tests in the rolling mill, where it was tested different material batches covering the large range of chemical compositions for this kind of steel. Mechanical tests were performed on samples taken from the practical tests in the rolling mill. From this tests the influence of chemical composition variation on the yeld strength and maximum stress was studied. As a result, we were able to determine the most likely range of temperatures for a minimization of hot strentgh, therefore also minimizing or eliminating the consequences of the reduction in the hot ductility due precipitation hardening of the matrix.

Utilizing the higher capacity steel in design can provide additional advantages to the concrete construction industry including a reduction of congestion, improved concrete placement, reduction in the required reinforcement and cross sections which would lead to savings in materials, shipping, and placement costs. Using high-strength reinforcement is expected to impact the design provisions of ACI 318 code and other related codes. The Applied Technology Council (ATC-115) report "Roadmap for the Use of High-Strength Reinforcement in Reinforced Concrete Design" has identified key design issues that are affected by the use of high-strength reinforcement. Also, ACI ITG-6, "Design Guide for the Use of ASTM A1035 Grade 100 Steel Bars for Structural Concrete" and NCHRP Report 679, "Design of Concrete Structures Using High-Strength Steel Reinforcement" have made progress towards identifying how code provisions in ACI 318 and AASHTO could be changed to incorporate high-strength reinforcement. The current research aims to provide a closer investigation of the behavior of beams reinforced with high-strength steel bars (including ASTM A615 Grade 100 and ASTM A1035 Grades 100 and 120) and high-strength concrete up to 12000 psi. Focus of the research is on key design issues including: ductility, stiffness, deflection, and cracking. The research includes an extensive review of current literature, an analytical study and conforming experimental tests, and is directed to provide a number of recommendations and design guidelines for design of beams reinforced with high-strength concrete and high-strength steel. Topics investigated include: strain limits (tension-controlled and compression-controlled, and minimum strain in steel); possible change for strength reduction factor equation for transition zone (Φ); evaluation of the minimum reinforcement ratio (þmin); recommendations regarding limiting the maximum stress for the high-strength reinforcement; and prediction of deflection and crack width at service load levels. Moreover, this research includes long-term deflection test of a beam made with high grade concrete and high-strength steel under sustained load for twelve months to evaluate the creep deflection and to insure the appropriateness of the current ACI 318 time-dependent factor, λ, which does not consider the yield strength of reinforcement and the concrete grade.

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The introduction of high strength concrete in construction demanded an assessment of the current methods of structural design. In the case of the slabs, the benefits brought about by concretes of higher strength could translate into design of slender sections. Theoretically these sections could be prone to excessive deflections. The flexural behaviour of such structural elements should be carefully assessed. The present thesis addresses a series of particular issues such as deflection at service loads, crack formation and development of tension stiffening and ductility. An experimental program on large-scale samples was conducted. Six one way and four two way slabs made of reinforced high strength concrete were tested under simulated and accurately measured equally distributed loads. Different loading stages were recorded. Crack formation, crack patterns and yield line disposition were observed. The main characteristics of concrete that influence the deflection behaviour were assessed based on collected data and on available literature results. Statistical methods were employed in order to refine empirical equations that help in the design of slabs. To improve the calculation of deflection of slabs a new equation for the effective moment of inertia was proposed. The new formula was integrated into a method of calculating deflection and verified against experimental results. Limits of the use of high strength concrete in slabs were investigated by means of a parametric study. This was designed to answer some questions as: which would be the most important characteristics of high-strength concrete that influence the design and up to what value of strength would the beneficial effect on deflection exhaust its effectiveness. Models based on the refined empirical equations for different concrete parameters were proposed. Another area that has been studied was the ductility of high strength concrete slabs. An analytical comparative study of the ductility of slabs reinforced with steel of different ductility class was conducted. Results were critically appraised and discussed.

Considerable amount of research was carried out into the properties and structural performance of high strength concrete for more than few decades. Whilst this research has produced relevant and useful results, there are several properties of high strength concrete like compressive and tensile strengths, stiffness, durability etc. that need to be evaluated and investigated to determine an accurate representation for the determination of different structural properties of beams made of high strength concrete. For this purpose, an investigation into the behaviour of beams made of higher concrete strengths has been carried out and conclusions drawn for the design of high strength concrete beams in flexure. Experimental data from previous research was considered for the study to establish some understanding of flexural behavior of HSC beams. A number of spreadsheets in Excel were developed using available data and various graphs were plotted to determine the accuracy of the code provisions for calculating the ultimate moment capacity of beams. A study on flexural ductility of beams has been carried out using a computer program FRMPHI which generates moment-curvature curves for the beams. Ductility has been studied using ductility factors. The influence of ductility on the value of the depth of neutral axis has been analysed and discussed. A chapter on the short-term deflection of simply supported high strength concrete beams under instantaneous deflections is presented. This chapter includes analysis of the available formula to calculate deflection to determine if these can be adopted for high strength concrete. Extensive ongoing research on the shear strength of beams by several researchers since many years has lead to the generation of a large body of knowledge. Although each author has analysed the data comparing them with existing relationships, the whole body of information has not been analysed to establish a statistical significance. In this study, regression analysis on experimental data collected from published research is carried a relationship between the different parameters affecting the shear strength of beams. The level of significance of the association between parameters influencing shear strength is also discussed.

Simple but still realistic physical models suitable for structural design of flat concrete plates and column footings with respect to punching are presented. Punching of a flat plate is assumed to occur when the concrete compression strain at the column edge due to the bending moment in the slab reaches a critical value that is considerably lower than the generally accepted ultimate compression strain 0.0035 for one-way structures loaded in bending. In compact slabs such as column footings the compression strength of the inclined strut from the load to the column is governing instead. Both the strain limit and the inclined stress limit display a size-effect, i.e. the limit values decrease with increasing depth of the compression zone in the slab. Due respect is also paid to increasing concrete brittleness with increasing compression strength. The influence of the bending moment means that flat plates with rectangular panels display a lower punching capacity than flat plates with square panels – a case that is not recognized by current design codes. As a consequence, punching shall be checked for each of the two reinforcement directions separately if the bending moments differ. Since the theory can predict the punching load as well as the ultimate deflection of test specimens with good precision, it can also treat the case where a bending moment, so called unbalanced moment, is transferred from the slab to the column. This opens up for a safer design than with the prevailing method. It is proposed that the column rotation in relation to the slab shall be checked instead of the unbalanced moment for both gravity loading and imposed story drift due to lateral loads. However, the risk for punching failure is a great disadvantage with flat plates. The failure is brittle and occurs without warning in the form of extensive concrete cracking and increased deflection. Punching at one column may even initiate punching at adjacent columns as well, which would cause progressive collapse of the total structure. A novel reinforcement concept is therefore presented that gives flat plates a very ductile behaviour, which eliminates the risk for punching failure. The performance is verified by tests with monotonic as well as cyclic loading. / QC 20100929

Nanocrystalline materials have generated immense scientific interest, primarily due to observations of significantly enhanced strength and hardness resulting from Hall-Petch grain size strengthening into the nano-regime. Unfortunately, however, most previous studies have been unable to present material strength measurements using established tensile tests because the most commonly accepted tensile test protocols call for specimen geometries that exceeded the capabilities of most nanocrystalline material synthesis processes. This has led to the development of non-standard mechanical test methodologies for the evaluation of miniature specimens, and/or the persistent use of hardness indentation as a proxy for tensile testing. This study explored why such alternative approaches can be misleading and revealed how reliable tensile ductility measurements and material strength information from hardness indentation may be obtained. To do so, an electrodeposition-based synthesis method to produce artifact-reduced specimens large enough for testing in accordance with ASTM E8 was developed. A large number of 161 samples were produced, tested, and the resultant data evaluated using Weibull statistical analysis. It was found that the impact of electroforming process control on both the absolute value and variability of achievable tensile elongation was strong. Tensile necking was found to obey similar processing quality and geometrical dependencies as in conventional engineering metals. However, unlike conventional engineering metals, intrinsic ductility (as measured by maximum uniform plastic strain) was unexpectedly observed to be independent of microstructure over the grain size range 10-80nm. This indicated that the underlying physical processes of grain boundary-mediated damage development are strain-oriented phenomena that can be best defined by a critical plastic strain regardless of the strength of the material as a whole. It was further shown that the HV = 3•σUTS expression is a reliable predictor of the relationship between hardness and strength for electrodeposited nanocrystalline materials, provided the material is ductile enough to sustain tensile deformation until the onset of necking instability. The widely used relationship HV = 3•σY was found to be inapplicable to this class of materials owing to the fact that they do not deform in an “ideally plastic” manner and instead exhibit plastic deformation that is characteristic of strain hardening behaviour.