ME 558 Fracture and Fatigue
Considerations in Design
Lecture 8
Strain - Life Approach
3/17/17
2
Concept of the Local Strain Life Approach
Straincontrolled
fatigue
specimen
Crack nucleation
and small crack
growth
Plastic zone
3/17/17
3
Fatigue Test Sample
Homework #2 - Solution
2-1. Calculate KI for a rectangular bar containing an edge crack loaded in three point
bending.
P = 35.0 KN; W = 50.8 mm; B = 25 mm; a/W = 0.2; S = 203 mm
P/2
P/2
S
a
P
W
2-2. Consider a material where KIC = 35 MPa
. Each of the fiv
ME 558 Fracture and Fatigue
Considerations in Design
Lecture 6
Rainflow Cycle Counting
D
2/22/17
Rainflow Cycle Counting
Identification of rainflow cycles as basic damaging
events
Hysteresis Loops
LOAD2.TXT-L1
5
1000
value (bits)
Stress
-4
0
2/22/17
time
ME 558 Fracture and Fatigue
Considerations in Design
Lecture 7
Todays Topics
Modification of S-N Curve
n
n
n
n
3/8/17
Surface Finish Factor
Size Effector
Stress-Based Fatigue Analysis and Design
n
Fatigue Strength Testing
n
Fatigue Limit Test
n
Mean Stres
ME 558 Fracture and Fatigue
Considerations in Design
Lecture 5
Importance of Fatigue in Engineering
Design
2/15/17
2
Importance of Fatigue in Engineering
Design
About 90 percent of mechanical failures are attributable to
fatigue - D. Walton, A Knowledge B
ME 558 Fracture and Fatigue
Considerations in Design
Lecture 4
Todays Topics
Chapter 3: Elastic-Plastic Fracture Mechanics
n
Apply to materials that exhibit time-independent nonlinear behavior
(plastic deformation).
n
n
n
Crack Tip Opening Displacement (C
ME 558 Fracture and Fatigue
Considerations in Design
Lecture 2
Todays Topics
Instability and R-Curve
Stress Analysis of Cracks
n
n
n
n
n
n
n
n
1/18/17
Failure Modes
Stress Intensity Factor
Relationship between K and Global Behavior
Effect of Finite Size
P
ME 558 Fracture and Fatigue
Considerations in Design
Lecture 3
2.8 Crack Tip Plasticity
Linear elastic stress analysis of sharp cracks predicts infinite
stresses at the crack tip. However, in real materials stresses at
the crack tip are finite because the
ME 558 Fracture and Fatigue
Considerations in Design
Lecture 1
Course Description
A comprehensive review of fracture and fatigue
processes in engineering material with emphasis
on mechanics instead of mechanisms of failure.
Design
methodology
based
on
fra
FATIGUE FROM VARIABLE
AMPLITUDE LOADING
Ali Fatemi - University of Toledo
All Rights Reserved
Chapter 9 Variable Amplitude Loading
1
FATIGUE FROM
VARIABLE AMPLITUDE LOADING
SPECTRUM LOADS AND CUMULATIVE DAMAGE
DAMAGE QUANTIFICATION AND THE CONCEPTS OF
D
MATERIAL BEHAVIOUR
All real bodies are deformable, meaning that their size and shape generally
change when loads are applied to them. If a problem is statically indeterminate,
the deformation of the components plays a crucial role in determining the distr
TORSION OF CYLINDRICAL BARS
We consider the case where a cylindrical bar (it may be solid or hollow) is
loaded by a twisting moment or torque T , as shown in Figure 1. For the cylindrical
bar, it is convenient to use cylindrical polar coordinates r, , z a
AXIAL LOADING (DETERMINATE PROBLEMS)
From Hookes law, an elastic bar in uniaxial tension will experience a tensile
strain
x
x =
,
(1)
E
where x is the tensile stress and E is Youngs modulus. We assume that the stress
is uniform over the cross-section A of
ME 211003 INTRODUCTION TO SOLID MECHANICS
Midterm Examination I Practice Examination
Attempt all questions
MULTIPLE CHOICE QUESTIONS
1. (1 point) The force in Figure 1 acts at the point B and has magnitude 400 N. Its
component Fx in the xdirection is:-
Fx
ECCENTRIC LOADING
In developing the bending formula
M
E
= = ,
I
y
R
(1)
we assumed that the beam was transmitting a bending moment M, but that the
axial force F was zero. In fact, the axial force transmitted by the cross-section can
be written as an integ
ME 382 Winter 2017
Homework 5
(Due Friday, February 17, 2017)
1.
Explain the following observations:
(i) Nickel can be strengthened by adding small hard particles of thoria.
(ii) At room temperature, the yield strength of pure silver (~50 MPa) is much
low
Due in class Thursday 01/26 (section 1 Capecelatro) Wednesday 01/25 (section 2 Johnsen)
Problem set #2 ME 320 Winter 2017
Problem 1: FM 2.48
Problem 2: FM 2.66
Problem 3: FM 2.78
1
Problem 4: FM 3.15
Problem 5
Two systems are filled with a liquid are show
Due in class Thursday 02/16 (section 1 Capecelatro) Wednesday 02/15 (section 2 Johnsen)
Problem set #5 ME 320 Winter 2017
Problem 1: F & M 2.33
Problem 2: F & M 4.12
Problem 3: F & M 4.35
1
Problem 4: F & M 4.43
Problem 5
2
Lecture 30 - Modeling creep
COMBINED MODELING OF CREEP, ELASTC AND PLASTIC DEFROMATION
Total strain consists of elastic + plastic +creep component
total = elastic + plastic + creep
n
For uniaxial case: elastic = /E ; plastic = A ;
d creep
dt
= o
o
n
Problem 5 Solution
The weight of this pressure vessel per unit length is given by:
w = gh(Dt) = (7700)(9.81)()(1)(0.05) = 11865.3 N/m
Therefore the maximum bending moment is Mmax =
the maximum axial stress is
max
zz
=
wL2
(11865.3)(6)2
=
= 53392.5 Nm, and
ME 382 Winter 2014
Homework 7
(Due Friday, November 4, 2014)
Use the von Mises yield criterion if appropriate
1.
2.
Given c = 0:296nm, a = 0:285nm, the volume of one unit cell
3.
a:
b:
c:
d:
e:
f:
100% martensite
80% martensite and 20% retained austenite
4. Leak-before-break Design Solution
(a) By HW4, we know that the critical pressure is Pc = 9.2 MPa. The required fracture toughness is then given by
1
KIc t
Pc R
2
r
> 9.0t KIc > 3Pc R
= 109.4 MPa m1/2
t
(b) Without the safety factor, we have
1
KIc t
Pc
ME 382 Winter 2016
Homework 6
Solution
1.
Copper alloys containing some beryllium can be hardened by precipitation / age
hardening. These alloys, known as beryllium copper or beryllium bronze, have
very high strengths, electrical conductivity, and low dam
Lecture 29 - Introduction to creep
CREEP
Instantaneous response to a load is elastic or plastic deformation
= f ( )
In general, all materials exhibit additional deformation with time
= f ( ,t )
This is known as creep
Importance of instantaneous response
ME 382 Fall 2016
Homework 5
(Due Friday, October 21, 2016)
1.
It has been shown (M.R. Staker, D.L. Holt, Acta Metal. Volume 20, Issue 4, April
1972, Pages 569579) that the shear strength k of a polycrystalline oxygen-free,
high-conductivity copper is pr
ME
382HOMEWORK
HOMEWORK 9 10
SOLUTIONS
ME
382
SOLUTION
p
1. (a) Based on the figure, when the stress intensity factor is 0.5 MPa pm, the crack
velocity is 10 4 m/s. when the stress intensity factor is 0.3 MPa m, the crack
velocity is 10 7.5 m/s.
da
= AK n
:wmo. kn an nr=< an waaw Hm x5925. nun worms :mwnnam <mpcm can cuwv amwu
m
cm unawnSMOEmnunn apxncwm nu wp<ma can
awvnrmqm or=<n
er<.a . -mn- . Mumqwu-
D=< armcva
mcww oamsav : a w nmx>v u >xmv m zhxxm xhxxm
:muam am: A u o c.omw Aq.m mo N.42
Huooanwnm