Modeling of an Interface Crack with Bridging Effects Between Tow Composite Layers
Authors
Henriksen, Thomas Bro ; Bak, Brian Lau Verndal
Term
4. term
Education
Publication year
2010
Pages
121
Abstract
Afhandlingen udvikler en praktisk procedure til at analysere og simulere delaminering (grænsefladerevner) i fiberkompositmaterialer, så ingeniører kan vurdere, om fundne fejl som tørpletter truer den strukturelle integritet og skal repareres. I stedet for enkle punktbaserede spændings- eller tøjningskriterier bygger proceduren på brudmekanik og beskriver, hvordan revnevækst afhænger af energifrigivelsesraten ved revnespidsen (Gc,0) og af revneåbningen, som påvirkes af fiberbroer bag spidsen. Fiberbroer skaber trækkrafter mellem revnefladerne, mindsker deres relative forskydning og øger den last, der skal til for at nå det kritiske tærskelniveau for udbredelse; denne effekt er medtaget indtil en stationær revnelængde er nået. Udbredelseskriteriet er G0 ≥ Gc,0, hvor G0 beregnes ud fra spændingsintensitetsfaktorer, som estimeres fra forskydningsfelter ved revnefladerne tæt på spidsen. For at estimere disse faktorer robust kombineres finitte element-analyse med en parametervurdering formuleret som et mindste kvadraters optimeringsproblem, løst med den konjugerede gradientmetode og søgning efter det gyldne snit. Da de klassiske udtryk for relativ revnefladeforskydning er uendelige serier af egenfunktioner, men ofte afkortes til den første term (kun gyldig meget tæt ved spidsen), udleder og anvender afhandlingen udtryk, der også inkluderer anden og tredje egenfunktion. Det muliggør pålidelige estimater med finitte elementer, der er 10–20 gange større end ved kun at bruge første egenfunktion; tilsvarende forbedringer bekræftes for ortotrope materialer. Tilgangen behandles desuden for grænsefladerevner mellem isotrope og anisotrope lag. Endelig viser en Double Cantilever Beam (DCB) simulering af revneudbredelse med fiberbroer i to ens ortotrope fibermaterialer god overensstemmelse med antagne testbaserede R-kurver i ren mod I (åbning) og mod II (glidning), mens den stationære brudmodstand overvurderes i en blandet mod.
This thesis develops a practical procedure to analyze and simulate delamination (interface cracks) in fibrous composite materials so engineers can judge whether detected defects, such as dry spots, threaten structural integrity and must be repaired. Rather than simple point stress or strain criteria, the procedure is based on fracture mechanics and captures how crack growth depends on the energy release rate at the crack tip (Gc,0) and on the crack opening influenced by fiber bridging behind the tip. Fiber bridging creates tractions between the crack faces, reduces their relative displacement, and raises the load required to reach the critical threshold for propagation; its effect is included until a steady‑state crack length is reached. The propagation criterion is G0 ≥ Gc,0, where G0 is computed from stress intensity factors estimated from crack‑face displacement fields near the tip. To estimate these factors robustly, the work combines finite element analysis with a parameter estimation formulated as a least‑squares optimization, solved by the conjugate gradient method with a golden‑section search. Because classical expressions for relative crack‑face displacement are derived as infinite series of eigenfunctions but are often truncated to the first term (valid only extremely close to the tip), the thesis derives and uses expressions that also include the second and third eigenfunctions. This enables reliable estimation with finite elements that are 10–20 times larger than when using only the first eigenfunction; similar improvements are confirmed for orthotropic materials. The approach is further examined for interface cracks between isotropic and anisotropic layers. Finally, a double cantilever beam (DCB) simulation of crack growth with fiber bridging in similar orthotropic fiber materials shows good agreement with assumed test‑based R‑curves in pure mode I (opening) and mode II (sliding), while steady‑state fracture resistance is overestimated in a mixed‑mode case.
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