CHEN E4630 Y - Topics in Soft Materials - Spring 2025
TAKE-HOME MIDTERM EXAMINATION
SYRENE-BUTADIENE RUBBER MATERIAL DESIGN
Monday March 24 12:01 PM - Friday March 28 5:00 PM
Suggestions/Comments:
Review the exam and clarify any questions with the instructor or TA ([email protected]; [email protected])
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SELECTION OF STYRENE BUTADIENE RUBBER FOR TIRE APPLICATIONS
Caruthers et al. published a report characterizing a broad range of styrene-butadiene rubbers (SBRs) using linear mechanical testing (Caruthers et al. J. POLYMER SCI., PART B: POL. PHYS. 2013, 51, 687-697; see Exams folder at the Files link on the course website). These data are to be used to make an assessment of the applicability of SBRs for automotive and bicycle tire ap- plications. In the following some relevant backround information about rubber materials is asked for. In addition, a reasonable set of mechanical criteria for tire applications is suggested. Based on these criteria make the assessment of the applicability of SBRs for tires based on the data reported by Carothers et al..
1. Work problem 2-4 in Aklonis. Based on this exercise, discuss criteria in terms of G' (w) and G'' (w) for rubber-like materials that would (i) provide an adequate elastic modulus at application conditions for auto-motive and bicycle tire applications, and (ii) restrict energy dissipation in such applications. (Hint: for (ii) what linear mechanical response function expressed in terms of G'
(w) and G'' (w) directly measures the rate of energy dissipation versus storage during cyclic loading?).
2. Estimate quantitatively the elastic modulus requirements needed for au-tomotive and bicycle tire applications from typical loads per tire and tire/pavement contact areas to stay within the limit of linear elastic be-havior of the tire material (say 10% strain). Set a second criterion that limits the rate energy dissipation to storage during cyclic loading for the applications to no more than 30%:
3. Estimate the the ranges of loading frequencies and temperatures associ- ated with the applications.
4. Read/skim the article by Caruthers et al. What is SRB rubber? (what polymer? show the repeat units involved). Explain the meaning of "cross-linking". How are the SBRs studied by Caruthers et al. crosslinked? Summarize the range of SBR materials studied by Caruthers et al.
5. What data (i.e. which figures) in Caruthers et al. allow assessment of whether any particular SBR studied is suitable mechanically at 20oC for the intended applications? Which material(s) among those studied most nearly satisfies the mechanical criteria set in parts 1-2. In what ways do these "optimal" materials fall short of the criteria set?
6. How would one determine the suitability of the material(s) selected in part 5). at other temperatures, both above and below 20oC ?
7. For the "optimal" SBR materials identified in part 5). how might their shortcomings be addressed ?