## Problem Set 6

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## Problem Set 6

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- School:
- Massachusetts Institute of Technology
- Course:
- 3 22 - Mechanical Behavior of Materials

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MIT OpenCourseWare http ocw mit edu 3 22 Mechanical Properties of Materials Spring 2008 For information about citing these materials or our Terms of Use visit http ocw mit edu terms Problem Set 6 Due Friday May 9 by 5 00 PM 1 Describe thoroughly yet concisely three general toughening mechanisms in materials Be sure to include an example of each and not to confuse yield strengthening with toughening For one mechanism show a fractograph and brie y note features in the fracture surface that illustrate how the mechanism works 2 Lowhaphandu and Lewandowski Scripta Mater 38 1811 1998 studied the effect of crack tip radius on the stress intensity factor at failure for a speci c material as summarized in the graph below Note that they call crack tip radius notch root radius and stress intensity factor at failure fracture toughness a Using Inglis analysis of stress at the tip of an elliptical hole calculate the stress at the crack tip as a function of applied stress for the largest and smallest crack tip radius considered This is an single edge crack with initial crack length a of 25 mm b Are your results from part a consistent with the results in the graph below i e con sistent with the fact that at the largest crack tip radius we measure has the largest stress intensity factor Explain why they are or are not consistent Courtesy of Elsevier Inc http www sciencedirect com Used with permission 3 For a single material which follows Paris Law steady state crack propagation with m 2 you have tested three components with initial crack sizes a which failed with nal crack sizes af listed in the table below a Assume the fatigue conditions of all components are uniaxial loading with R 1 at a maximum stress of 100 MPa and a frequency f of 10 Hz Draw t for two complete loading cycles and also draw the representative volume elements and associated stress states at the minimum and maximum t b Compare the differences in fatigue lifetimes for the three components Explain your ndings in

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