Mechanical Behavior of Plastics

Readings

This page contains a calendar of reading assignments by lecture session.

List of references for the course (PDF)

Textbooks

Ward, I. M., and J. Sweeney. An Introduction to the Mechanical Properties of Solid Polymers. 2nd ed. New York, NY: John Wiley & Sons, 2004. ISBN: 9780471496267.

Roylance, David. Mechanics of Materials. New York, NY: John Wiley, 1995. ISBN: 9780471593997.

Modules in Mechanics of Materials

Preamble to Mechanics Modules (PDF)

Chapter 1: Tensile Response of Materials

The modules in this section will outline some of the basic concepts of materials mechanical response by restricting the geometry to a case of simple uniaxial tension. Many of the atomistic and mechanistic concepts in our materials-oriented approach to solid mechanics can be introduced in this way, without the mathematical and conceptual complications that more realistic gemoetries entail. Subsequent modules will extend these concepts to geometrically more complicated situations, and introduce gradually the mathematical language used by the literature of the field to describe them.

1. Introduction to elastic response
2. Atomistics of elasticity
3. Introduction to composites
4. Stress-strain curves

Chapter 2: Simple Tensile and Shear Structures

In this and subsequent modules, we seek to apply the concepts of materials response outlined in our discussion of Simple Tensile Response to actual structures of the sort encountered in engineering design. We will restrict ourselves initially to situations still having relatively simple geometries, specifically trusses, pressure vessels, and shafts loaded in torsion. This is done partly to introduce new concepts without excessive detail, but these structural types are far from being of academic interest only. As it is very often true that the best design is the simplest design, these simple structures make up a large part of modern construction.

5. Trusses
6. Pressure vessels
7. Shear and torsion

Chapter 3: General Concepts of Stress and Strain

In extending the direct method of stress analysis presented in previous modules to geometrically more complex structures, it will be convenient to have available somewhat more general mathematical statements of the kinematic, equilibrium, and constitutive equations; this is the objective of the present chapter. These equations also form the basis for more theoretical methods in stress analysis, as well as for numerical approaches such as the finite element method. We will also seek to introduce some of the notational schemes used widely in the technical literature for such entities as stress and strain. Depending on the specific application, both index and matrix notations can be very convenient; these are described in a separate module.

8. Kinematics
9. 9. Equilibrium
10. 10. Tensor transformations
11. 11. Constitutive relations

Chapter 4: Bending

This modules in this section will develop relations between stresses, deflections, and applied loads for beams and flat plates subjected to bending loads. This will be done using the direct method employed in Module 7 for circular shafts in torsion. However, bending problems have a higher order of dimensionality than twisted shafts, and it will be convenient to use the more general formulations developed in Modules 8 - 11. In particular, pseudovector-matrix notation will allow easy extension of beam concepts to flat plates.

12. Shear and bending moment diagrams
13. Stresses in beams
14. Beam displacements
15. Laminated composite plates

Chapter 5: General Stress Analysis

The results presented in earlier modules for trusses, beams, and other simple shapes provide much of the information needed in design of load-bearing structures. However, materials and structural engineers routinely need to estimate stresses and deflections in geometrically more irregular articles. This is the function of stress analysis, by which we mean the collection of theoretical and experimental techniques that goes beyond the direct-analysis approach used up to now. This is a career field in its own right, and these modules will limit themselves to outlining only a few of its principal features.

16. Closed-form solutions
17. Experimental solutions
18. Finite element analysis
19. Linear viscoelasticity

Chapter 6: Yield and Fracture

20. Yield and plastic flow
21. Dislocation basis of yield and creep
22. Statistics of fracture
23. Introduction to fracture mechanics
24. Fatigue

Appendices

1. Material properties (PDF), Table of properties (PDF), props (CSV)
2. Matrix and index notation (PDF)
3. List of symbols (PDF)
4. Unit conversion factors (PDF)

Software

1. Mohr’s circle (JAVA™ Applets)
2. strs3d - Stress transformations (PDF), PC-executable version: strs3d.exe (EXE)
3. Plate - Laminated plates (PDF), PC-executable version: plate.exe (EXE)

Calendar Reading Assignments

LEC #	TOPICS	READINGS
1	Introduction, overview of polymers
2	Chemical composition	Ward, pp. 1-4.
3	Structure	Ward, pp. 4-17. IUD paper: Roylance, David. “Assessment of Olefin-Based IUD Tail Strings.” Journal of Applied Biomaterials 4 (1993): 289-301. Spherulite paper: Starkweather, Howard W. Jr., and Richard E. Brooks. “Effect of Spherulites on the Mechanical Properties of Nylon 66.” Journal of Applied Polymer Science 1 (1959): 236-239.
4	Elastic response	Module 1, pp. 1-8.
5	Strain	Ward, pp. 20-22 and 25-26. Module 8, pp. 1-7.
6	Stress	Ward, pp. 18-20. Module 9, pp. 1-5.
7	Transformations of stress and strain	Module 10, pp. 1-4 and 8-10. Ballistic fibres Cunniff article: Cunniff, Philip M., Margaret A. Auerbach, Eugene Vetter, and Doetze J. Sikkema. “High Performance ‘M5’ Fiber for Ballistics / Structural Composites.” Paper AO-04 at the 23rd Army Science Conference.
8	Hookean elasticity	Ward, pp. 23-24. Module 11, pp. 1-6.
9	Gaussian chain statistics	Ward, pp. 32-36.
10	Rubber elasticity	Ward, pp. 36-40. Module 2, pp. 7-15.
11	Elastomer mechanics	Module 6.
12	Introduction to linear viscoelasticity	Ward, pp. 45-47. Module 19, pp. 1-3.
13	Creep and stress relaxation	Ward, pp. 48-50. Module 19, pp. 4-6.
14	Quiz 1
15	Dynamic response	Ward, pp. 62-65. Module 19, pp. 6-8. Boyer article: Boyer, R. F. “Dependence of Mechanical Properties on Molecular Motion in Polymers.” Polymer Engineering and Science 8 (1968): 161-185.
16	The Maxwell spring-dashpot model	Ward, pp. 55-58. Module 19, pp. 8-11.
17	Standard linear solid	Ward, pp. 58-60. Module 19, pp. 11-16.
18	Wiechert solid, Boltzman superposition	Ward, pp. 51-55. Module 19, pp. 17-19.
19	Effect of temperature	Module 19, pp. 19-23.
20	Effect of temperature (cont.)	Ward, pp. 84-93 and 97-102. Struik article: Struik, L. C. E. “Physical Aging in Plastics and Other Glassy Materials.” Polymer Engineering and Science 17 (1977): 165-173.
21	Multiaxial stresses	Module 19, pp. 23-26. Ultrasonic heating study (PDF)
22	Stress analysis: Superposition	Module 19, pp. 26-28.
23	Stress analysis: Correspondence principle	Module 19, pp. 28-31. Fiber impact study
24	Composite materials, rule of mixtures	Ward, pp. 141-149. Module 3, pp. 1-4.
25	Mechanics of composites	Ward, pp. 149-154, Module 3, pp. 4-5. Composites degradation article: Kumar, Bhavesh G., Raman P. Singh, and Toshio Nakamura. “Degradation of Carbon Fiber-reinforced Epoxy Composites by Ultraviolet Radiation and Condensation.” Journal of Composite Materials 36 (2002): 2713-2733.
26	Quiz 2
27	Composite laminates: Anisotropy and transformations	Module 15, pp. 1-6. Gillham article: Gillham, John K. “Formation and Properties of Thermosetting and High Tg Polymeric Materials.” Polymer Engineering and Science 26 (1986): 1429-1433. Epoxy cure study (PDF)
28	Laminates: Plate bending	Module 15, pp. 6-13.
29	Laminates: Temperature and viscoelastic effects	Module 15, pp. 11-16. Tuttle-Brinson article: Tuttle, M. E., and H. F. Brinson. “Prediction of the Long-Term Creep Compliance of General Composite Laminates.” Experimental Mechanics 26 (1986): 89-102.
30	Yield	Ward, pp. 211-221. Module 4, (all).
31	Yield: Multiaxial stresses	Ward, pp. 222-224. Module 20, pp. 1-5.
32	Yield: Effect of hydrostatic stress, crazing	Ward, pp. 224-229 Module 20, pp. 5-8. Sternstein-Ongchin article: Sternstein, S. S., and L. Ongchin. “Yield Criteria for Plastic Deformation of Glassy High Polymers in General Stress Fields.” Polymer Preprints 10 (1969): 1117-1124.
33	Yield: Effect of rate and temperature	Ward, pp. 237-241. Module 20, pp. 8-10.
34	Fracture: The Zhurkov model	Ward, pp. 269-271. Zhurkov article: Zhurkov, S. N. “Kinetic Concept of the Strength of Solids.” International Journal of Fracture Mechanics 1 (1965): 311-322. Roylance article: Roylance, David K. “Characterization of Polymer Deformation and Fracture.” Chapter 13 in Applications of Polymer Spectroscopy. Edited by Edward G. Brame. New York, NY: Academic Press, 1978. ISBN: 9780121254506.
35	Fracture: The Griffith model	Ward, pp. 246-253. Module 23, pp. 1-7. Williams article: Williams, M. L. “Fracture in Viscoelastic Media.” Fundamental Phenomena in the Materials Sciences 4 (1967): 23-32.
36	Fracture: Crack-tip stresses, stress intensity factor	Module 23, pp. 7-9.
37	Quiz 3
38	Fracture: Effect of specimen geometry	Module 23, pp. 10-13.
39	Fracture: J-integral and viscoelasticity	ABS article: Lu, Ming-Luen, Chang-Bing Lee, and Feng-Chih Chang. “Fracture Toughness of Acrylonitrile-Butdiene-Styrene by J-Integral Methods.” Polymer Engineering and Science 35 (1995): 1433-1439.