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- Catalog Description
- 519 Fracture Mechanics. II; 3 cr. Introduction to the mechanics of fracture of linear and nonlinear materials. Crack stress and deformation fields; stress intensity factors; crack tip plastic zone; fracture toughness testing; energy release rate; J-integral. Criteria for crack growth initiation/stability; application to design. P: EMA 214, 304, or 306/307.
- Course Prerequisite(s)
- EMA 214, 303, 304, or ME 306
- Prerequisite knowledge and/or skills
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EMA 519 focuses on a specific structural failure mode, that of fracture. The stress/strain fields surrounding crack tips are more complicated than those associated with continuous media, so students are advised to have a first course in mechanics of materials before attempting this more advanced topic.
- Textbook(s) and/or other required material
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Textbook:
T. L. Anderson, Fracture Mechanics: Fundamentals and Applications, 3rd Edition. CRC Press, 2004.
Reference:
H. L. Edwards and R. Wanhill, Fracture Mechanics, Edward Arnold, 1986.
- Course objectives
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Course Objectives: It is the instructor's intention to...
explain the importance of crack/flaw analysis in structural design and safety assessments and illuminate its wide range of applicability.
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teach/reinforce the rigorous fundamentals of solid mechanics for plane problems.
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teach the derivation of stress, strain and deformation fields near cracks in linear and nonlinear materials.
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explain how these stress/strain/deformation field results relate to fracture criteria and to an understanding of their limitations.
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illustrate how the major fracture criteria are applied in design and safety assessments and teach students how to use these, including in open-ended problems.
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impart to the students: a deep understanding of the major results and criteria underpinning modern fracture mechanics; the assumptions behind and limitations of these; and a practiced ability to apply these to practical situations.
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give students practice in written and oral explanation, and in justification of their thinking, on challenging technical concepts.
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Course Outcomes: Students must have the ability to...
explain the importance of flaw analysis in structural design and safety assessments.
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describe the broad range of applicability of fracture mechanics concepts.
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understand and use the governing equations of plane linear elasticity and plasticity in Cartesian and polar coordinates, explain the conditions under which they can be used and how to solve plane problems involving them.
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derive some of the plane governing equations and solve some simple plane problems.
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derive crack tip stress, strain and displacement fields.
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use the crack tip results to understand and determine limitations on various fracture criteria.
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determine stress intensity factors for several important example cases via superposition and other methods such as the J-integral.
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derive estimates of size and shape of crack tip plastic zones in Modes I, II and III.
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analyze numerous specific problems requiring application of fracture criteria and comment on their validity.
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explain what can be learned by application of fracture mechanics in several open-ended problems, and justify conclusions.
- Topics covered
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Design and analysis of engineering structures: general failure modes
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Examples of important fracture mechanics applications (buttressed by myriad articles from the popular press)
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Theoretical fracture strength of an unflawed crystalline solid.
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Stresses near an elliptical hole; Orowan (stress-based) fracture criterion
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Griffith (energy-based) fracture criterion; energy release rate in linear and nonlinear elastic materials; stability of crack growth in brittle materials
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Microscopic fracture mechanisms
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Charpy impact test; ductile-to-brittle transition temperature phenomenon
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Introduction to the mechanics of solids (concepts needed for crack analysis)
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Introduction to Linear Elastic Fracture Mechanics (LEFM): crack tip stress, strain and displacement fields in linear elastic materials (Modes I, II and III); the stress-intensity factor, K; Irwin's fracture criterion; design philosophy using K_Ic - specific examples
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Stress intensity factors for important geometries; methods for finding K
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Estimates of crack plastic zones in ductile materials; 3D effects
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Fracture toughness (K_Ic) testing; experimental results; limitations of LEFM
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The compliance method; experimental determination of compliance
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Introduction to fracture mechanics of nonlinear materials: the J-integral; the Hutchinson-Rice-Rosengren (HRR) crack tip fields; the J_Ic fracture criterion; J_Ic testing; J-controlled crack growth and the crack growth resistance (JR) curve; application of J to anisotropic and heterogeneous materials.
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One-dimensional crack-tip nonlinear zone models
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Fracture of composites and other advanced materials; mixed-mode fracture
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Application of fracture mechanics concepts in the analysis of fatigue crack growth
- Class/laboratory schedule
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EMA 519 meets two times per week for 75 minute lectures.
- Contribution of course to meeting the professional component
- This course contributes primarily to the students' knowledge of engineering topics, and does provide design experience.
The following statement indicates which of the following considerations are included in this course: economic, environmental, ethical, political, societal, health and safety, manufacturability, sustainability.
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Fracture, like fatigue, is a failure mode that frequently occurs without warning and with catastrophic results to life and property. Health and safety are strong underlying themes in EMA 519, with students spending significant time learning the nature and prevention of fracture.
- Relationship of course to undergraduate degree program objectives and outcomes
- This course primarily serves students in the department. The information below describes how the course contributes to the undergraduate program objectives.
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EMA 519 is appropriate as a senior technical elective or graduate student breadth elective. In terms of the EMA program objectives, it is focused to provide fundamental education via problem-solving, design-oriented team projects and communication in a subject (fracture mechanics) crucial to those planning a career in mechanics and astronautics.
- Assessment of student progress toward course objectives
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The nature of the assessment tools provide students with the opportunity to give an oral defense of their results and respond to questions.
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Regular class participation in which students are asked to explain orally how they would attack/solve/assess the situation under discussion.
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Challenging problem sets are assigned, that are collected and graded, in which students perform the derivations, analyses, practical problem solutions and assessments described in Course Outcomes.
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In-class, closed-book examinations, in which students must show: mastery of fundamental concepts; deep understanding of key derivations; ability to analyze practical problems and justify their analyses; understanding of the limitations of the methods they use.
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Students regularly are requested to present their solutions of certain homework and exam problems to the class, and to explain and defend their analyses, conclusions and interpretations. Class members are invited to question and debate their fellow presenters.
- Person(s) who prepared this description
