journal article·2013-10

Temperature dependence of cohesive laws for an epoxy adhesive in Mode I and Mode II loading

Tomas Walander, Anders Biel, Ulf Stigh

International Journal of Fracture· Volume 183· Issue 2
Publisher page

Abstract

The influence of the temperature on the cohesive laws for an epoxy adhesive is studied in the glassy region, i.e. below the glass transition temperature. Cohesive laws are derived in both Mode I and Mode II under quasi-static loading conditions in the temperature range $$-30\le T \le 80\,\circ $$ C. Three parameters of the cohesive laws are studied in detail: the elastic stiffness, the peak stress and the fracture energy. Methods for determining the elastic stiffness in Mode I and Mode II are derived and evaluated. Simplified bi-linear cohesive laws to be used at any temperature within the studied temperature range are derived for each loading mode. All parameters of the cohesive laws are measured experimentally using only two types of specimens. The adhesive has a nominal layer thickness of 0.3 mm and the crack tip opening displacement is measured over the adhesive thickness. The derived cohesive laws thus represent the entire adhesive layer as having the present layer thickness. It is shown that all parameters, except the Mode I fracture energy, decrease with an increasing temperature in both loading modes. The Mode I fracture energy is shown to be independent of the temperature within the evaluated temperature span. At $$80\,\circ $$ C the Mode II fracture energy is decreased to about 2/3 of the fracture energy at $$-30\,\circ $$ C. The experimental results are verified by finite element analyses.
Source: openaire · Quality: candidate unverified · Source record ↗

Research context

OpenAlex topics: Mechanical Behavior of Composites · Structural Analysis of Composite Materials · Epoxy Resin Curing Processes

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

References (40)

Show source-provided references
1. Alfredsson KS (2004) On the instantaneous energy release rate of the end-notch fexure adhesive joint specimen. Int J Solids Struct 41:4787–480710.1016/j.ijsolstr.2004.03.008 ↗
2. Alfredsson KS, Biel A, Leffler K (2003) An experimental method to determine the complete stress-deformation relation for a structural adhesive layer loaded in shear. In: Proceedings of the 9th international conference on the mechanical behaviour of materials, Geneva, Switzerland 2002
3. Alfredsson KS, Stigh U (2012) Stability of beam-like fracture mechanics specimens. Eng Fract Mech 89:98–11310.1016/j.engfracmech.2012.04.027 ↗
4. Andersson T, Biel A (2006) On the effective constitutive properties of a thin adhesive layer loaded in peel. Int J Fract 141:227–24610.1007/s10704-006-0075-6 ↗
5. Andersson T, Stigh U (2004) The stress-elongation relation for an adhesive layer loaded in modus I using equilibrium of energetic forces. Int J Solids Struct 41:413–43410.1016/j.ijsolstr.2003.09.039 ↗
6. Banea MD, da Silva LFM, Campilho RDSG (2012) Mode II fracture toughness of adhesively bonded joints a function of temperature: experimental and numerical study. J Adhes 88:534–55110.1080/00218464.2012.660835 ↗
7. Biel A, Walander T, Stigh U (2012) Influence of edge-boundaries on the cohesive behaviour of an adhesive layer. In: Proceedings of ASME IMECE2012-89534, Houston, TX, USA10.1115/IMECE2012-89534 ↗
8. Carlberger T, Biel A, Stigh U (2009) Influence of temperature and strain rate on cohesive properties of a structural epoxy adhesive. Int J Fract 155:155–16610.1007/s10704-009-9337-4 ↗
9. Carlsson LA, Gillespie JW, Pipes RB (1986) On the analysis and design of the end notch flexure (ENF) specimen for mode II testing. J Compos Mat 20:594–60410.1177/002199838602000606 ↗
10. Carlsson LA, Gillespie JW (1989) Mode II interlaminar fracture of composites. In: Friedrich K (ed) Application of fracture mechanics to composite materials, composite materials series 6. Elsevier, Amsterdam, pp 113–15710.1016/B978-0-444-87286-9.50008-5 ↗
11. Chai H (2004) The effects of bond thickness, rate and temperature on the deformation and fracture of structural adhesives under shear loading. Int J Fract 130:497–51510.1023/B:FRAC.0000049504.51847.2a ↗
12. Cherepanov GP (1967) The propagation of cracks in a continuous medium. J Appl Math Mech 31:503–51210.1016/0021-8928(67)90034-2 ↗
13. Davidson BD, Sun X (2005) Effects of friction, geometry, and fixture compliance on the perceived toughness from three-and four-point bend end-notched flexure tests. J Reinf Plast Compos 24:1611–162810.1177/0731684405050402 ↗
14. Fernberg S, Berglund L (2001) Bridging law and toughness characterization of CSM and SMC composites. Compos Sci Technol 61:2445–245410.1016/S0266-3538(01)00167-1 ↗
15. Högberg JL, Sørensen BF, Stigh U (2007) Constitutive behaviour of mixed mode loaded adhesive layer. Int J Solids Struct 44:8335–835410.1016/j.ijsolstr.2007.06.014 ↗
16. Johnson RA, Wichern SW (1992) Applied multivariate statistical analysis, 3rd edn. Prentice Hall, Englewood Cliffs
17. Kinloch AJ (1987) Adhesion and Adhesives—Science and Technology. Chapman and Hall, London10.1007/978-94-015-7764-9 ↗
18. Klarbring A (1991) Derivation of a model of adhesively bonded joints by the asymptotic expansion method. Int J Eng Sci 29:493–51210.1016/0020-7225(91)90090-P ↗
19. Kruskal WH, Wallis WA (1952) Use of ranks in one-criterion variance analysis. J Am Stat Assoc 47:583–62110.1080/01621459.1952.10483441 ↗
20. Leffler K, Alfredsson KS, Stigh U (2007) Shear behaviour of adhesive layers. Int J Solids Str 44:530–54510.1016/j.ijsolstr.2006.04.036 ↗
21. Li R, Jiao J (2000) The effects of temperature and aging on Young’s moduli of polymeric based flexible substrates. Proc Int Soc Opt Eng 1999, 2000
22. Li S, Thouless MD, Waas AM, Schroeder JA, Zavattieri PD (2005) Use of a cohesive-zone model to analyze the fracture of a fiber-reinforced polymer-matrix composite. Compos Sci Technol 65:537–54910.1016/j.compscitech.2004.08.004 ↗
23. Li S, Thouless MD, Waas AM, Schroeder JA, Zavattieri PD (2006) Mixed-mode cohesive-zone models for fracture of an adhesive bonded polymer-matrix composite. Eng Fract Mech 73:64–7810.1016/j.engfracmech.2005.07.004 ↗
24. Mall S, Kochhar NK (1986) Finite element analysis of end notch flexure specimen. NASA contractor report 178113
25. Martin RH, Davidson BD (1999) Mode II fracture toughness evaluation using four point bend, end notched flexure test. Plast Rubber Compos Process Appl 28:401–40610.1179/146580199101540565 ↗
26. Marzi S, Biel A, Stigh U (2011) On experimental methods to investigate the effect of layer thickness on the fracture behaviour of adhesively bonded joints. Int J Adhes Adhes 31:840–85010.1016/j.ijadhadh.2011.08.004 ↗
27. Mohammad I, Liechti KM (2000) Cohesive zone modelling of crack nucleation at bimaterial corner. Mech Phys Solids 48:735–76410.1016/S0022-5096(99)00052-6 ↗
28. Nilsson F (2001) Fracture mechanics—from theory to application. Dep Sol Mech, KTH, Stockholm
29. Olsson P, Stigh U (1989) On the determination of the constitutive properties of the interphase layers—an exact solution. Int J Fract 41:71–7610.1007/BF00018870 ↗
30. Rice JR (1968) A path independent integral and the approximate analysis of strain concentrations by notches and cracks. ASME J Appl Mech 33:379–38510.1115/1.3601206 ↗
31. Schmidt P (2008) Modelling of adhesively bonded joints by an asymptotic method. Int J Eng Sci 46:1291–132410.1016/j.ijengsci.2008.06.008 ↗
32. Sørensen BF (2002) Cohesive law and notch sensitivity of adhesive joints. Acta Materialia 50:1053–106110.1016/S1359-6454(01)00404-9 ↗
33. Suo Z, Bao G, Fan B (1992) Delamination R-curve phenomena due to damage. J Mech Phys Solids 40:1–1610.1016/0022-5096(92)90198-B ↗
34. Stigh U (1988) Damage and crack growth analysis of the double cantilever beam specimen. Int J Fract 37:R13–1810.1007/BF00017826 ↗
35. Stigh U, Andersson T (2000) An experimental method to determine the complete stress-elongation relation for a structural adhesive layer loaded in peel. In: Williams JG and Pavan A (eds) Fracture of polymers. composites and adhesives, ESIS publication 27, pp 297–30610.1016/S1566-1369(00)80026-6 ↗
36. Stigh U, Alfredsson KS, Biel A (2009) Measurement of cohesive laws and related problems. In: Proc ASME, IMECE2009-10474, Lake Buena Vista, Florida10.1115/IMECE2009-10474 ↗
37. Stigh U, Alfredsson KS, Andersson T, Biel A, Carlberger C, Salomonsson K (2010) Some aspects of cohesive models and modelling with special application to strength of adhesive layers. Int J Fract 165:149–16210.1007/s10704-010-9458-9 ↗
38. Walander T (2009) System for measurement of cohesive laws. Dissertation, University of Skövde
39. Walander T, Biel A, Stigh U (2012) An evaluation of the temperature dependence of cohesive properties for two structural epoxy adhesives. In: Proceedings of the 19th European Conference Fractures, Kazan, Russia
40. Yang QD, Thouless MD (2001) Mixed-mode fracture analysis of plastically-deforming adhesive joints. Int J Fract 110:175–18710.1023/A:1010869706996 ↗