### Course Meeting Times

Lectures: 3 sessions / week, 1 hour / session

### Description

3.91 Mechanical Properties of Polymers is one of MIT’s principal graduate subjects in polymeric materials. It is a “core” subject in the MIT interdepartmental Program in Polymer Science and Technology (PPST), and one of the elective subjects in the doctoral Bio - and Polymer Program of the Department of Materials Science and Engineering. 3.91 was developed originally by Prof. F. J. McGarry in the 1960’s, and has been offered continually at MIT ever since. Prof. D. Roylance has co-taught the subject since the mid-1970’s, and became the sole instructor with Prof. McGarry’s retirement in June 2002.

As its name implies, 3.91 is aimed at presenting the concepts underlying the response of polymeric materials to applied loads. These will include both the molecular mechanisms involved and the mathematical description of the relevant continuum mechanics. It is dominantly an “engineering” subject, but with an atomistic flavor. The subject content will follow approximately that of the Ward text:

- Polymer structure
- Deformation of elastic solids
- Rubber-like elasticity
- Linear viscoelasticity
- Composite materials and laminates
- Yield
- Fracture

The subject carries 3-0-9 credit, so approximately three hours of outside work should follow each lecture hour. These outside hours will include a thorough reading of various sections of the Ward text or Roylance modules as assigned in the Schedule, and often one or more engineering problems. The reading assigned for a given day should be complete before class, and the assigned problem should be turned in at the next class meeting. (Occasionally your personal schedule may force you to delay a day or two, but try to avoid this.) No penalty will be assessed for the **occasional** one-day-late submission. Grading will be based on the quality of the submitted problems, the vigor of your in-class discussion, and the three quizzes.

Student collaboration on homework is permitted and encouraged, but all work to be submitted should then be worked out and written up on your own. Copying from “bibles” or other such sources is cheating. Computer solutions are encouraged when appropriate; ‘Maple® and MATLAB®’ are excellent for many of the assigned problems.

There are no formal recitations, but you are encouraged to make frequent use of the Instructor’s office hours for assistance or just informal discussion.

### 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.

### Schedule

Each assignment is due during the next class session.

LEC # | TOPICS | KEY DATES |
---|---|---|

1 | Introduction, overview of polymers | Homework 1 out |

2 | Chemical composition | |

3 | Structure | |

4 | Elastic response | Problem set 1.8 out |

5 | Strain | Problem set 8.4 out |

6 | Stress | |

7 | Transformations of stress and strain | Problem set 10.6 out |

8 | Hookean elasticity | Problem set 11.2 out |

9 | Gaussian chain statistics | |

10 | Rubber elasticity | Problem set 2.7 out |

11 | Elastomer mechanics | Problem set 6.8-6.9 out |

12 | Introduction to linear viscoelasticity | Problem set 19.1-19.2 out |

13 | Creep and stress relaxation | |

14 | Quiz 1 | |

15 | Dynamic response | Problem set 19.4 out |

16 | The Maxwell spring-dashpot model | |

17 | Standard linear solid | Problem set 19.6-19.8 out |

18 | Wiechert solid, Boltzman superposition | Problem set 19.11 out |

19 | Effect of temperature | Problem set 19.17-19.18 out |

20 | Effect of temperature (cont.) | Problem set 19.19 out |

21 | Multiaxial stresses | Problem set 19.20 out |

22 | Stress analysis: Superposition | |

23 | Stress analysis: Correspondence principle | Problem set 19.21-19.22 out |

24 | Composite materials, rule of mixtures | Problem set 3.1-3.2 out |

25 | Mechanics of composites | Problem set 3.3 out |

26 | Quiz 2 | |

27 | Composite laminates: Anisotropy and transformations | Problem set 15.1-15.2 out |

28 | Laminates: Plate bending | Problem set 15.5 out |

29 | Laminates: Temperature and viscoelastic effects | |

30 | Yield | Problem set 4.8 out |

31 | Yield: Multiaxial stresses | |

32 | Yield: Effect of hydrostatic stress, crazing | |

33 | Yield: Effect of rate and temperature | Problem set 20.10 out |

34 | Fracture: The Zhurkov model | |

35 | Fracture: The Griffith model | |

36 | Fracture: Crack-tip stresses, stress intensity factor | |

37 | Quiz 3 | |

38 | Fracture: Effect of specimen geometry | |

39 | Fracture: J-integral and viscoelasticity |