3.1 Introduction
Learning Objectives:
1) Introduce to micromechanics of a lamina
2) Recognize that 13 parameters need to be found for the unidirectional lamina
Videos
Title: Introduction to Micromechanics of a Lamina
Learning Objectives: Find why we need to conduct microeconomics of a lamina, and identify the needed properties for a unidirectional lamina.
Summary: Discover the importance of studying the micromechanics of a lamina. Identify the 13 properties required for a unidirectional lamina. Understand the significance of defining volume fractions and density.
Slide Shows
Worked Out Examples
None
Handouts
None
Flashcards
None
Quiz
3.2 Volume and Mass Fractions, Density and Void Content
Learning Objectives:
1) Develop concepts and compute volume fraction of fiber and matrix
2) Develop concept and compute weight fraction (mass fraction) of fiber and matrix
3) Compute density of composite
4) Compute void fraction in composites
5) Enumerate how voids affect the properties of a lamina
Title: Volume and Weight Fractions, and Density of a Composite; Theory
Learning Objectives: After watching this video, you will be able to define volume fractions, weight fractions, and density of a composite.
Summary: Learn how to determine the volume and weight fractions of fiber and matrix, as well as the density of a composite. These are required for calculating the elastic moduli and hygrothermal properties of the unidirectional lamina. Additionally, find the relationship between the volume and weight fractions of the fiber and the matrix.
Title: Volume and Weight Fractions, and Density of a Composite: Example
Learning Objectives: After watching this video, you will be able to calculate volume fractions, weight fractions, and density of a composite.
Summary: Via an example, learn how to find the density and weight fractions of a composite.
Title: Voids, Void Fractions, Derivation, Experimental, Example
Learning Objectives: After watching this video, you will be able to find the effect of voids on composite properties, derive and calculate void fractions, and experimentally find void fractions.
Summary: Learn what properties get affected by voids, how to define and derive the formula for void fraction, and how to experimentally find void fractions.
Slide Shows
Worked Out Examples
Problem 3.2 Solution [PDF]
Problem 3.3 Solution [PDF]
Handouts
None
Flashcards
Volume and Mass Fractions, Density and Void Content Slideshow
Quiz
3.3 Evaluation of Four Elastic Moduli
Learning Objectives:
1) Develop formulas for four elastic moduli based on mechanics of materials approach
2) Develop formulas for four elastic moduli based on Halpin-Tsai approach
Videos
Title: Longitudinal Young’s Modulus, E1
Learning Objectives: Derive and calculate the longitudinal Young’s modulus of a unidirectional lamina.
Summary: Learn how to derive and calculate the longitudinal Young’s modulus of a unidirectional lamina. The derivation is based on distributing the forces carried by the fiber and the matrix. Find the ratio of the forces taken by the fiber and the matrix.
Title: Transverse Young’s Modulus, E2
Learning Objectives: Derive and calculate the transverse Young’s modulus of a unidirectional lamina.
Summary: Learn how to derive and calculate the transverse Young’s modulus of a unidirectional lamina. The derivation is based on the transverse displacement in the fiber and the matrix.
Title: Major Poisson’s ratio, ν12
Learning Objectives: Derive and calculate the major Poisson’s ratio of a unidirectional lamina.
Summary: Learn how to derive and calculate the major Poisson’s ratio of a unidirectional lamina.
Title: In-plane shear modulus, G12
Learning Objectives: Derive and calculate the shear modulus of a unidirectional lamina.
Summary: Learn how to derive and calculate the shear modulus of a unidirectional lamina.
Title: Halpin Tsai Equations for Elastic Moduli
Learning Objectives: Calculate the four elastic moduli of a unidirectional lamina based on Halpin Tsai Equations.
Summary: The mechanics of materials approach does not predict the transverse Young’s moduli and in-plane shear modulus accurately. See how a semi-empirical approach using Halpin Tsai equations is used to calculate the four elastic moduli of a unidirectional lamina.
Slide Shows
Worked Out Examples
Problem 3.6 [PDF]
Why are Halpin-Tsai Equations called semi-empirical? [PDF]
Worked Out Video Examples
Title: A Worked Out Example about the In-Plane Shear Modulus
Learning Objectives: Find out what the in-plane shear modulus is for polymer matrix composites using mechanics of materials approach and Halpin Tsai equations.
Summary: Find out what the in-plane shear modulus is for polymer matrix composites using mechanics of materials approach and Halpin Tsai equations.
Handouts
None
Flashcards
Evaluation of Four Elastic Moduli Slideshow
Quiz
3.4 Ultimate Strengths of a Unidirectional Lamina
Learning Objectives:
1) Develop formulas for the five strength parameters of a unidirectional lamina
2) Learn experimental methods of finding elastic moduli and strength properties of a unidirectional lamina
Videos
Title: Introduction to Ultimate Strengths of a Unidirectional Lamina
Learning Objectives: Enumerate the five ultimate strengths one needs to know of a unidirectional Lamina.
Summary: The video segment introduces the ultimate strengths of a unidirectional lamina, focusing on five key strength parameters: longitudinal tensile strength, longitudinal compressive strength, transverse tensile strength, transverse compressive strength, and in-plane shear strength. These parameters are essential for understanding the micromechanics of a unidirectional lamina, which requires 13 parameters in total, including elastic moduli, thermal expansion coefficients, and moisture expansion coefficients. The segment explains the significance of these strength parameters and how they relate to the directions parallel and perpendicular to the fibers, providing a foundational understanding of the material’s mechanical properties.
Title: Ultimate Longitudinal Tensile Strength of a Unidirectional Lamina
Learning Objectives: Estimate the ultimate longitudinal tensile strength of a unidirectional lamina using theory. Outline the test procedure to find ultimate longitudinal tensile strength of a unidirectional lamina experimentally.
Summary: Derive the formula for the longitudinal tensile strength of a unidirectional lamina. Also, see how minimum and critical fiber volume fractions are found. See an example of how these parameters are calculated. Also, see how the ASTM standards are used to experimentally find the longitudinal tensile strength of a unidirectional lamina. The video of ASTM standard experimental setup and method is here.
Title: Experimentally Find Ultimate Longitudinal Tensile Strength of a Unidirectional Lamina
Learning Objectives: Estimate the ultimate longitudinal tensile strength of a unidirectional lamina using experiments.
Summary: Coming soon
Title: Ultimate Longitudinal Compressive Strength of a Unidirectional Lamina
Learning Objectives: Estimate the ultimate longitudinal compressive strength of a unidirectional lamina using theory. Outline the test procedure to find ultimate longitudinal compressive strength of a unidirectional lamina experimentally. Enumerate why the theoretical and experimental results do not match well for this strength parameter.
Summary: In this video, we explore the concept of longitudinal compressive strength in unidirectional lamina. This is a measure of how much compressive stress a lamina can withstand along the fibers before failing. We start by discussing the different ways a material can fail under compression, such as the matrix (the material holding the fibers together) failing, the fibers themselves buckling, or the bond between the fibers and the matrix breaking. We then calculate the ultimate compressive strength. This is done by considering four different failure modes and taking the minimum value as the ultimate strength. Next, we look at an example using a glass epoxy lamina with 60% fiber volume fraction. We calculate the compressive strength based on the given properties of the fibers and the matrix. We also discuss how to experimentally determine the compressive strength using the IITRI compression test, which involves compressing a specimen and measuring its response. Finally, we compare the theoretical results with experimental data and discuss why there might be differences. Factors such as irregular fiber spacing, imperfect bonding, and misalignment of fibers can affect the results.
Title: Experiments to Find Ultimate Longitudinal Compressive Strength of a Unidirectional Lamina
Learning Objectives: Steps for Composites Fixture Assembly for Testing per ASTM D3410.
Summary: This video demonstrates the assembly of a jig for testing composite materials according to ASTM D3410 and ISO 14126 Method 1B. The jig consists of a base, wedges, alignment pins, and a compression specimen. The video shows the step-by-step process of assembling the jig and preparing the specimen for testing.
Title: Ultimate Transverse Tensile Strength of a Unidirectional Lamina
Learning Objectives: Estimate the ultimate transverse tensile strength of a unidirectional lamina using theory. Outline the test procedure to find ultimate transverse tensile strength of a unidirectional lamina experimentally.
Summary: In this video, we explore the transverse tensile strength of a unidirectional lamina. We start by modeling the problem and then work through an example. We also discuss how to determine the transverse tensile strength experimentally. The video covers the application of stress perpendicular to the fibers, the calculation of ultimate stress, and the use of representative volume elements. Additionally, we delve into the relationship between the displacement in the composite, fiber, and matrix, and how to derive the ultimate tensile strength using various formulas. Finally, we demonstrate an example calculation and explain the experimental setup for measuring transverse tensile strength.
Title: Ultimate Transverse Compressive Strength of a Unidirectional Lamina
Learning Objectives: Estimate the ultimate transverse compressive strength of a unidirectional lamina using theory. Outline the test procedure to find ultimate transverse compressive strength of a unidirectional lamina experimentally.
Summary: In this video, we explore the transverse compressive strength of a unidirectional lamina. We start by modeling the problem and then work through an example. We also discuss how to determine the transverse compressive strength experimentally. The video covers the application of stress perpendicular to the fibers, the calculation of ultimate compressive stress, and the use of representative volume elements. Additionally, we delve into the relationship between the displacement in the composite, fiber, and matrix, and how to derive the ultimate compressive strength using various formulas. Finally, we demonstrate an example calculation and explain the experimental setup for measuring transverse compressive strength.
Title: Ultimate In-Plane Shear Strength of a Unidirectional Lamina
Learning Objectives: Estimate the ultimate in-plane shear strength of a unidirectional lamina using theory. Outline the test procedure to find ultimate in-plane shear strength of a unidirectional lamina experimentally.
Summary: In this video, we explore the shear strength of a unidirectional lamina. We start by modeling the problem and then work through an example. We also discuss how to determine the shear strength experimentally. The video covers the application of the shear stress, the calculation of ultimate shear stress, and the use of representative volume elements. Additionally, we delve into the relationship between the displacement in the composite, fiber, and matrix, and how to derive the ultimate shear strength using various formulas. Finally, we explain the experimental setup for measuring shear strength.
Title: Experimental Way of Finding Ultimate In-Plane Shear Strength of a Unidirectional Lamina
Learning Objectives: Find one of the ways Ultimate Shear Strength and In-Plane Shear Modulus of Unidirectional Lamina experimentally.
Summary: See how the ASTM D5379 V-Notched Beam Testing (losipescu) of CFRP works.
Title: Several short videos of the uniaxial test
Slide Shows
Worked Out Video Examples
Title: An Example Problem to Find the Ultimate Longitudinal Tensile Strength of a Unidirectional Intraply Lamina.
Learning Objectives: Estimate the ultimate longitudinal tensile strength of a unidirectional intraply lamina.
Summary: Replacing glass fibers by graphite fibers – effect on modulus, strength and density. A unidirectional lamina is made of glass/epoxy (called Gl/Ep) with a 30% matrix volume fraction. Without changing the matrix volume fraction, some of the glass fibers are now replaced by graphite fibers so that the longitudinal Young’s modulus gets doubled. Let’s call this new hybrid composite Gl/Gr/Ep. What is the volume fraction of the graphite fibers you would need to accomplish this? What is the percentage change in the density of the Gl/Gr/Ep composite over the Gl/Ep composite? Does it increase or decrease? Calculate the longitudinal tensile strength of the Gl/Ep and Gl/Gr/Ep unidirectional laminas. Are they different even when the ultimate strengths of glass and graphite fibers are the same?
Handouts
None
Flashcards
Ultimate Strengths of a Unidirectional Lamina Slideshow
Quiz
3.5 Coefficients of Thermal Expansion
Learning Objectives:
1) Derive formulas for the longitudinal coefficient of thermal expansion
2) Derive formulas for the transverse coefficient of thermal expansion
Videos
Title: Longitudinal Coefficient of Thermal Expansion: Derivation
Learning Objectives: Derive the formula for the longitudinal coefficient of thermal expansion.
Summary: Learn how the formula for the longitudinal coefficient of thermal expansion is derived. See what it is dependent on and how it is derived based on mechanical stresses caused in the fiber and the matrix due to temperature change.
Title: Coefficients of Thermal Expansion: Example
Learning Objectives: Calculate the longitudinal and transverse coefficient of thermal expansion.
Summary: Learn how to calculate the longitudinal and transverse coefficient of thermal expansion for a composite lamina.
Slide Shows
Worked Out Examples
Derivation of Transverse Thermal Expansion Coefficient [PDF] This derivation is optional but you do need to know the formula inside-out
Handouts
None
Flashcards
Coefficients of Thermal Expansion Slideshow
Quiz
3.6 Coefficients of Moisture Expansion
Learning Objectives:
1) Derive formulas for the longitudinal coefficient of moisture expansion
2) Derive formulas for the transverse coefficient of moisture expansion
Videos
Title: Longitudinal Coefficient of Moisture Expansion: Derivation
Learning Objectives: Derive the formula for the longitudinal coefficient of moisture expansion.
Summary: Learn how the formula for the longitudinal coefficient of moisture expansion is derived. See what it is dependent on and how it is derived based on mechanical stresses caused in the fiber and the matrix due to moisture absorption and deabsorption. Learn how the formula simplifies if the fiber is not capable of absorbing or deasorbing moisture or when the fiber Young’s modulus is much higher than that of the matrix.
Title: Coefficients of Moisture Expansion: Example
Learning Objectives: Calculate the longitudinal and transverse coefficient of moisture expansion.
Summary: Learn how to calculate the longitudinal and transverse coefficient of moisture expansion for a composite lamina where the fiber does not absorb or deabsorb moisture.
Slide Shows
Worked Out Examples
None
Handouts
None
Flashcards
Coefficients of Moisture Expansion Slideshow
Quiz