me 582 advanced materials science chapter 2 macromechanical...
TRANSCRIPT
ME 582 Advanced Materials Science • Department of Mechanical Engineering Dr. Jan Gou
ME 582 Advanced Materials Science
Chapter 2 Macromechanical Analysis of a Lamina(Part 2)
Dr. Jan GouLaboratory for Composite Materials Research
Department of Mechanical EngineeringUniversity of South Alabama, Mobile, AL 36688
ME 582 Advanced Materials Science • Department of Mechanical Engineering Dr. Jan Gou
HW #3
2.35
2.38
2.43
Due Day: 6:00 PM, 10/04/2006, Wednesday.
ME 582 Advanced Materials Science • Department of Mechanical Engineering Dr. Jan Gou
Strength Failure Theories of an Angle Lamina
The failure theories are generally based on the normal and shear strengths of a unidirectional lamina.
An isotropic material generally has two strength parameters: normal strength and shear strength.
In the case of a unidirectional lamina, the five strength parameters are
Longitudinal tensile strengthLongitudinal compressive strengthTransverse tensile strengthTransverse compressive strengthIn-plane shear strength
ultT )( 1σ
ultC )( 1σ ultC )( 1σ
ultC )( 2σ
ultT )( 2σ
ult)( 12τ
ME 582 Advanced Materials Science • Department of Mechanical Engineering Dr. Jan Gou
Maximum Stress Failure Theory
The lamina is considered to be failed if
Each component of stress does not interact with each other.
ME 582 Advanced Materials Science • Department of Mechanical Engineering Dr. Jan Gou
Example 2.13
ME 582 Advanced Materials Science • Department of Mechanical Engineering Dr. Jan Gou
Example 2.13
ME 582 Advanced Materials Science • Department of Mechanical Engineering Dr. Jan Gou
Example 2.13
ME 582 Advanced Materials Science • Department of Mechanical Engineering Dr. Jan Gou
Example 2.13
ME 582 Advanced Materials Science • Department of Mechanical Engineering Dr. Jan Gou
Maximum Strain Theory
The lamina is considered to be failed if
ME 582 Advanced Materials Science • Department of Mechanical Engineering Dr. Jan Gou
The ultimate strains can be found from the ultimate strength parameters and the elastic moduli, assuming the stress-strain response is linear until failure.
For the maximum strain failure theory, no interactions occurs between various components of strain.
The maximum stress failure theory and the maximum failure straintheory give different results because the local strains in a lamina include the Poisson’s ratio.
If the Poisson’s ratio is zero in the unidirectional lamina, the two failure theories will give identical results.
Maximum Stress and Strain Failure Theories
ME 582 Advanced Materials Science • Department of Mechanical Engineering Dr. Jan Gou
Tsai-Hill Failure Theory
Based on the distorsion energy theory, they proposed that a lamina has failed if
This theory is based on the interaction failure theory.
The components G1 - G6 of the strength criteria depend on the failure strength.
ME 582 Advanced Materials Science • Department of Mechanical Engineering Dr. Jan Gou
Components of Tsai-Hill Failure Theory
ME 582 Advanced Materials Science • Department of Mechanical Engineering Dr. Jan Gou
Components of Tsai-Hill Failure Theory
Solution:
ME 582 Advanced Materials Science • Department of Mechanical Engineering Dr. Jan Gou
Tsai-Hill Failure Theory – Plane Stress
ME 582 Advanced Materials Science • Department of Mechanical Engineering Dr. Jan Gou
Tsai-Hill Failure Theory
Unlike the maximum strain and maximum stress failure theories, the Tsai-Hill failure theory considers the interaction among the three unidirectional lamina strength parameter.
The Tsai-Hill failure theory does not distinguish between the compressive and tensile strengths in its equation. This can result in underestimation of the maximum loads that can be applied when compared to other failure theory.
Tsai-Hill failure theory underestimates the failure stress because the transverse strength of a unidirectional lamina is generally much less than its transverse compressive strength.
ME 582 Advanced Materials Science • Department of Mechanical Engineering Dr. Jan Gou
Modified Tsai-Hill Failure Theory
ME 582 Advanced Materials Science • Department of Mechanical Engineering Dr. Jan Gou
Tsai-Wu Failure Theory
Tsai-Wu applied the failure theory to a lamina in plane stress. A lamina is considered to be failed if
The components H1 – H66 of the failure theory are found using the five strength parameters of a unidirectional lamina.
ME 582 Advanced Materials Science • Department of Mechanical Engineering Dr. Jan Gou
Components of Tsai-Wu Failure Theory
Solution:
ME 582 Advanced Materials Science • Department of Mechanical Engineering Dr. Jan Gou
Components of Tsai-Wu Failure Theory
Solution:
ME 582 Advanced Materials Science • Department of Mechanical Engineering Dr. Jan Gou
Components of Tsai-Wu Failure Theory
Solution:
ME 582 Advanced Materials Science • Department of Mechanical Engineering Dr. Jan Gou
Determination of H12
ME 582 Advanced Materials Science • Department of Mechanical Engineering Dr. Jan Gou
Determination of H12
ME 582 Advanced Materials Science • Department of Mechanical Engineering Dr. Jan Gou
Empirical Models of H12
ME 582 Advanced Materials Science • Department of Mechanical Engineering Dr. Jan Gou
Example 2.19
ME 582 Advanced Materials Science • Department of Mechanical Engineering Dr. Jan Gou
Example 2.19
ME 582 Advanced Materials Science • Department of Mechanical Engineering Dr. Jan Gou
Example 2.19
ME 582 Advanced Materials Science • Department of Mechanical Engineering Dr. Jan Gou
Example 2.19
ME 582 Advanced Materials Science • Department of Mechanical Engineering Dr. Jan Gou
Example 2.19
ME 582 Advanced Materials Science • Department of Mechanical Engineering Dr. Jan Gou
Experimental Results and Failure Theories
Tsai-Wu compared the results from various failure theories to some experimental results. He considered an angle lamina subjected to a uniaxial load in the x-direction.
The failure stresses were obtained experimentally for tensile and compressive stresses for various angles of the lamina.
ME 582 Advanced Materials Science • Department of Mechanical Engineering Dr. Jan Gou
Stresses in the Material Axes
ME 582 Advanced Materials Science • Department of Mechanical Engineering Dr. Jan Gou
Strains in the Material Axes
ME 582 Advanced Materials Science • Department of Mechanical Engineering Dr. Jan Gou
Experimental Results and Failure Theories
ME 582 Advanced Materials Science • Department of Mechanical Engineering Dr. Jan Gou
Experimental Results and Failure Theories
ME 582 Advanced Materials Science • Department of Mechanical Engineering Dr. Jan Gou
Experimental Results and Failure Theories
ME 582 Advanced Materials Science • Department of Mechanical Engineering Dr. Jan Gou
Experimental Results and Failure Theories
ME 582 Advanced Materials Science • Department of Mechanical Engineering Dr. Jan Gou
Hygrothermal Stress-Strain Relationship
For a unidirectional lamina
Thermally induced strains:
Moisture induced strains:
ME 582 Advanced Materials Science • Department of Mechanical Engineering Dr. Jan Gou
For a unidirectional lamina
Hygrothermal Stress-Strain Relationship
ME 582 Advanced Materials Science • Department of Mechanical Engineering Dr. Jan Gou
For an angular lamina
Hygrothermal Stress-Strain Relationship
Thermally induced strains:
Moisture induced strains:
ME 582 Advanced Materials Science • Department of Mechanical Engineering Dr. Jan Gou
Transformation of CTE
For an angular lamina
ME 582 Advanced Materials Science • Department of Mechanical Engineering Dr. Jan Gou
Transformation of Coefficients of Moisture Expansion
For an angular lamina
ME 582 Advanced Materials Science • Department of Mechanical Engineering Dr. Jan Gou
Example 2.20
ME 582 Advanced Materials Science • Department of Mechanical Engineering Dr. Jan Gou
Example 2.20
ME 582 Advanced Materials Science • Department of Mechanical Engineering Dr. Jan Gou
Example 2.20
ME 582 Advanced Materials Science • Department of Mechanical Engineering Dr. Jan Gou
Example 2.20