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<\/figure>\n\n\n\nSo if your composite microstructure is always exactly like\nthose two \u201cblocks,\u201d then Rule of Mixtures is a great option for you, and you\ndon\u2019t even need to bother reading the rest of this post.<\/p>\n\n\n\n
However, we all know most composites don\u2019t look like this.\nEven continuous fiber composites, whose properties are often estimated using\nRule of Mixtures, have a different type of microstructure. But this isn\u2019t just\nabout \u201cthe looks.\u201d The geometric assumptions affect how the local field variables\nare estimated. Therefore, using the wrong geometry, even for \u201csimilar\u201d\ncomposites such as continuous fibers, can bring errors to local stress\/strain\nfields and consequently affect their properties and failure predictions. <\/p>\n\n\n\n
Why doesn’t it work? <\/h2>\n\n\n\n
It doesn\u2019t matter how sophisticated your failure model is. Your results will still be inaccurate because their inputs \u2013 the local fields \u2013 were based on incorrect initial assumptions. It is like building a fancy house on top of a weak foundation \u2013 it is a waste of time and money. <\/strong><\/p>\n\n\n\n So let\u2019s understand the root of these inaccuracies. <\/p>\n\n\n\n In the first model, the assumption is that under uniaxial tension, the strains on the fibers and resins are the same, <\/strong>while the stresses are proportional to each constituent\u2019s moduli.<\/strong> That is not quite true, but luckily, fiber mechanical properties are normally one order of magnitude larger than resin properties. Therefore, it is common for the axial direction response to be fiber-dominated with the influence of resin being quite small. Under those circumstances, the experimental results show acceptable agreement with the first model equation. <\/p>\n\n\n\n This explains why Rule of Mixtures can still be reasonably\napplied in practice to axial response of continuous fibers despite the\ngeometric inaccuracies of the model, even for this given composite. However,\nthe bigger problem lies in the prediction of transverse direction properties,\nas we discuss below. <\/p>\n\n\n\n In the second model, the extra assumption is reversed:\nthe stresses on the\nfibers and the resin are the same, while strains are now inversely proportional to each\nconstituent\u2019s moduli.\nHowever, this time you can\u2019t count luck, as this model is much more inaccurate\nthan the first one. This is partially because the fibers will \u201cprotect\u201d\nportions of the resin from stress while causing other resin areas to be\nover-stressed, as seen in the below image of the fringe patterns of microscale\nstress distribution. <\/p>\n\n\n\n So much for equivalent stresses among constituents \u2013 the\nstresses are not constant, not even throughout the same constituent! But the\nconsequences of that go beyond simply predicting wrong moduli. <\/p>\n\n\n\n In reality, damage initiates sooner than one would predict\nby using Rule of Mixtures. Therefore, your Rule of Mixtures-based design is not\nso safe anymore. <\/strong><\/p>\n\n\n\n So what? You can always overdesign, right? Wrong! <\/p>\n\n\n\n In an ever-competitive market, overdesign is each day more\nthe last resort. In fact, with tight margins and increasing competition, small\namounts of overdesign can mean the difference between winning or losing a\nclient for the competition. Sometimes, even the business feasibility of\nemploying composites at all can be compromised because of overdesign. Not\nsurprisingly, as the cost of overdesign can be quite high. <\/p>\n\n\n\nThe problem with overdesigning<\/h2>\n\n\n\n
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