Experimental Stress Analysis
Class Notes
by
Poornesh Kumar K, PhD
Dept of Mechanical Engineering
Assistant Professor
NITK
(ME412 )
Credit and Grading
Credits: 3
Grading:
15% for Quiz – Two quizzes during the coursework
15% for Presentation – the topic shall be related to this course
30% for Mid-Term exam
40% for Finals
Syllabus - Content
1. Introduction to Stress Analysis – 4 hr
2. Stress and Strain – Review – 2 hrs
3. Fracture Mechanics – Review - 4 hrs
1. Strain Gauges – demo – 3 hrs
Quiz – 1
Mid-Term
1. Strain Gauges – 6 hrs
2. Photoelasticity – 7 hrs
Quiz – 2
Presentation – 6hrs
Finals
1. Introduction to Stress Analysis
Stress analysis can be carried out based on:
1. Analytical Approach
- Continuum Mechanics - Theory
2. Numerical Approach
- FEM
3. Experimental Approach
- Local Method and Global Method
1. Introduction to Stress Analysis
a. Point-by-Point Method (Locally resolved)
- Contact and Non-contact Extensometers
- Capacitive Transducers
Example:-
b. Globally resolved
- Photoelasticimetry
Photoelastic effect
Experiment to examine the spread of mechanical stress
Utilizes artificial anisotropy caused by mechanical deformation of a material
By observing the material through a polarizing filter, one can detect the typical
interference patterns.
The denser the stripes are in a location, the greater the mechanical stress is in
that location
- Moire Method
Moiré patterns appear when superposing two transparent layers containing
correlated opaque patterns. The case when layer patterns comprise straight or
curved lines is called line moiré.
Moiré effect is a visual perception that occurs when viewing a set of lines or dots
that is superimposed on another set of lines or dots, where the sets differ in
relative size, angle, or spacing.
Example:
- Holographic Method
This is based on the laser light interference between the hologram of an
undeformed to deformed body
Truths Vs Hype - Literally
Case Study – Automotive Components
E
D
B
C
C
B
A
D
E
Wrong!
A
Truth!
F
Standard FEA
Inclusion
Damage
Stress
(from
most
severe
(from
most severe
(from highest
to lowest) to less severe) to less severe)
B
A
D
E
D
A
A
E
C
D
C
E
C
B
B
Highest
Modern FEA answer
Lowest
Mises
Stress
D
B
E
A
F
C
Initial
Damage
Porosity
C
E
F
B
E
D
D
A
B
F
A
C
Modern Materials Science answer
True answer
maximum von
Mises Stress
model
failure predicted by
damage model under
performance with
distribution of initial
porosity
Stress – Different Scales
Stress – The Origins
Traction – Continuum Scale
Cauchy Stress Principle
Stress – Equilibrium Equations
Previous Class – on black board
Important things to Note: Derivation of equilibrium equation
Displacement/Strain Relations
Static Determinance
There are there possibilities
a. A structure is not sufficiently restrained (fewer reactions than d.o.f.) degrees
of freedom ⇒ DYNAMICS
b. Structure is exactly (or “simply”) restrained (# of reactions = # of d.o.f.)
⇒ STATICS (statically determinate)
c. Structure is overrestrained (# reactions > # of d.o.f.)
⇒STATICALLY INDETERMINATE
…must solve for reactions simultaneously with stresses, strains, etc. in this case, you
must employ the stress-strain equations
--> Overall, this yields for elasticity:
15 unknowns
and
6 strains = εmn
6 stresses = σmn
3 displacements = um
15 equations
3 equilibrium (σ)
6 strain-displacements (ε)
6 stress-strain (σ -ε)
NOTABLE POINT: The first two sets of equations are “universal” (independent of the
material) as they depend on geometry (strain-displacement) and equilibrium
(equilibrium). Only the stress-strain equations are dependent on the material.