Hi there so. I’d like to talk to you now about chapter 16 on composites materials journals, journals on composite materials and this will be our last online lecture given by me for the semester. So yeah and here you see some images of some common composites materials journals, journals on composite materials that you probably come in contact with before concrete here on the left and fiberglass here on the right so they’re really common building materials and so it’s important that you be familiar with them so a composite materials journals, journals on composite materials is defined as a combination of two or more individual materials and composites materials journals, journals on composite materials can be natural or synthetic. An example of a natural composite materials journals, journals on composite materials is shown here the bone in our body is actually a composite materials journals, journals on composite materials material so is wood by the way anyway bone is made from a hard and brittle material called hydroxyapatite which is mainly calcium phosphate in a soft and flexible material called collagen. Which is a protein now. The design goal for composites materials journals, journals on composite materials is to obtain a more desirable combination of properties. This is actually called the principle of combined action when you combine properties of two different materials to become a better more desirable combination. For whatever you’re trying to do for example you might want a low-density material that’s also high-strength like say for example a carbon fiber composite materials journals, journals on composite materials now composites materials journals, journals on composite materials are multi-phase materials. And a lot of them now are artificially made for various structures and building materials. You have two phase types at least and a composite materials journals, journals on composite materials material you have your matrix and that’s your continuous material. That kind of binds it all together and then you have your dispersed material. It’s discontinuous and it’s surrounded by the matrix. The purposes of your matrix phase are to transfer stress to the dispersed phase which is usually your strong material and it also protects the dispersed phase from the environment so some typical examples are metal matrix composites materials journals, journals on composite materials or MMC’s ceramic matrix composites materials journals, journals on composite materials composites materials journals, journals on composite materials RC sieze and polymer matrix composites materials journals, journals on composite materials or PMC s the dispersed rays can serve a variety of purposes. It can increase your yield strength.
Increase your tensile strength or increase resistance to creep. It can also increase your fracture toughness or increase. Your elastic modulus comes in three types that can be particles fibers or structure structural for the dispersed phase. Here’s some of the classification of these composites materials journals, journals on composite materials so of the three that I already said the particle reinforce the fiber reinforced or the structural composites materials journals, journals on composite materials . They can have subdivisions so under particle reinforced. You can have your large particles like a like a cement for example or a concrete in cement or it can be dispersion strengthened with small particles that are in the order of 10 to 100 nanometers. Your fiber reinforced can be continuous which means long fibers and they can be aligned or they can be discontinuous fibres meaning that they can be very short and among the discontinuous they can be either aligned or randomly oriented and your structural composites materials journals, journals on composite materials fall under two broad categories the laminates and the sandwich signals which. We’ll talk more about later. So here’s some examples of your particle reinforced. So at top here. We have one that we kind of already cover. It’s asteroid ice steel so that one has the matrix of the ferrite which is the alpha phase. And it’s more ductile and then the particles are cement tight and those are brittle and hard so in this case your matrix being embedded with these little cementite particles. The cementite particles themselves actually act as barriers to slip which makes the material harder than the alpha phase would be by itself. The next example here is the cemented. Carbide this is actually often called a ceramic metal composite materials journals, journals on composite materials or a. Thermage on the one shown here is a large particle. And here you have your tungsten carbide particles in your cobalt matrix in this case your turns sign by particles are very brittle and hard whereas your matrix the COBOL. Cobalt is more ductile and tough now in particular. This disk composite materials journals, journals on composite materials is often used for cutting steels.
The tungsten carbide. Particles are really brittle and hard if you tried to cut the steel with just. The tungsten carbide without being in the matrix so it would probably fracture because it is so brittle and so the cobalt provides ductility and toughness to material that prevents fracture and then here at the bottom. There is automobile tire rubber which is a matrix of rubber which is compliant and sort of springy material combined with carbon. Black carbon. Black is what you get when you burn hydrocarbons and it forms these little almost spherical particles that are small. This is example here. The automobile tire tire rubber is an example of the dispersion strength and composite. Because you can see here. These little carbon black particles are very small. What happens is when you add the carbon black to the rubber. The tire becomes a lot more tough and resistant to tears and a lot harder material than it would be without. The carbon black oftentimes tires are about fifteen to thirty percent by weight carbon black material another really common material that we talked about is concrete in terms of composite materials journals, journals on composite materials materials. I’ve actually posted several videos about concrete because it is one of the more important and commonly used composite materials journals, journals on composite materials materials on the planet so concrete is not the same as cement concrete is actually a mixture of a gravel and sand and cement so concrete is gravel sand cement and water and the sand and gravel. Actually fill the voids. Between the gravel particles you can reinforce concrete with steel rebar or remesh and that increases the strength so that even if the cement matrix cracks over time the materials still stay. Strong sand supports the load. You can also pre-stress your concrete by putting a rebar or a remash and play sitting under tension while the concrete sets and then attends the release of tension after setting places the concrete in a constant state of compression which makes it stronger and to fracture concrete and applied tensile stress has to exceed the compressive stress.
That it’s already in. You can also post tension it by putting nuts on the ends to place the concrete under compression now moving on to the particle reinforced formula for the elastic modulus. You can see here that the elastic modulus e for the composite materials journals, journals on composite materials with the subscript sub. C can be put between an upper and a lower limit okay and this is actually known as the rule of mixtures between them. It says that your your material properties for your matrix your sub. M here your M subscript here and your particulate. P the P subscript here is actually going to be a mixture and it will fall between the upper limit equation here east of C is equal to V M times M plus VT P times V P. Here these stands for the volume fraction mini stands for the modulus as I said and then the lower limit expression is 1 over EC is equal to V M over m plus VP over e P. And so you can see here. The expressions for the upper and lower limits are shown here in red and blue and the values the actual values for this composite materials journals, journals on composite materials material fall in between the upper and the lower limits. According to the rule of mixtures this expression can also be applied to other properties. Not just the modulus for example but it could be used to express the electrical conductivity where you in replace the ease in the equation with the signals for the conductivity or the thermal conductivity K where you replace the es with caves so it gives you a good expression. General expression for estimating what material properties of the composite materials journals, journals on composite materials disease now the next classification of composites materials journals, journals on composite materials is actually technologically. Probably one of the most important types of composites materials journals, journals on composite materials and that’s fiber reinforced composites materials journals, journals on composite materials and fibers are very very strong and tension. So they provide significant strength improvement to the composite materials journals, journals on composite materials for example you might be familiar with fiberglass which is continuous glass. Filaments and a polymer matrix near the glass fibers.
Provides strength and stiffness while the polymer matrix holds the fibers in place for checks the fiber of surfaces and transfers Road to the fibers. You can have different fiber types one is whiskers which are thin single crystals with large link to diameter ratios and some examples of those are graphite. Silicon nitride silicon carbine. There’s also some of those that are being applied to nanotechnology where you have a carbon fiber and carbon nanotube whisker type fibers. They have a high crystalline perfection. These whiskers they’re extremely strong. In fact they’re the strongest known however they can be very expensive and they can be difficult. To disperse. You can also have fiber fiber types which are poly crystalline or amorphous. And those are generally polymers or ceramics. For example alumina aramid glass boron ultra high molecular weight. Polyethylene those are all fibers that can be used in these composites materials journals, journals on composite materials . Mathari you can have wire fiber types. Those are metals like steel molybdenum and tungsten and this provides strong resistance to creep the way the fibers are aligned. Really dictates a lot of their performance. There’s two types there’s the aligned. Continuous or the discontinuous from the continuous are the long fibers. Very long fibers. There are about 30 times the critical length. Which is a property that will get you in a minute and these continuous fibers. Because they are long they basically have to be aligned in the longitudinal direction. So here you have. Longitudinally aligned fibers the performance of these aligned. Continuous fibers can be very different. Depending upon which direction the stress is applied if it’s applied in a longitudinal direction they’ll be much much stronger than if the stress is applied in the transverse direction for the discontinuous or short fibers. You can either have aligned or random orientation of the fibers. You might want random orientation if you’re not really sure what directions the stress is going to be applied in or if it’s just as likely the stress to come from any direction.
Here’s some examples of the fiber reinforced composites materials journals, journals on composite materials and images of what they might look like for example. Here’s the metal wires type composite materials journals, journals on composite materials and you can see here that you have these metal fibers embedded in the metal matrix and that provides a strong resistance to create and also more strength. You can also have here. An example of ceramic with glass with silicon carbide whisker fibers and that’s formed by a glass slurry and you can see that there’s actually a pretty big spread in between the elastic modulus for the glass or for the silicon carbide. And so you would get a much stronger and much higher elastic modulus for the material when you mix those fibers in. Here’s some examples of some discontinuous. Fibres this one shows an example of carbon fibers. Invented in a polymer resin matrix. These can be used in disc brakes. Gas turbine engine flaps and missile nose cones. I’ve actually posted another external video on carbon fibers because they are one of the more important new types of composites materials journals, journals on composite materials out there and I encourage you to watch that. Also you can have the fibers align in the plane or they could be aligned randomly in three dimensions or they could be aligned so in the images that’s shown here. This is random in two dimensions but aligned along the plane now the length of the fiber that you use is very very important for their fibers performance. So there’s something called the critical fiber links for effective stiffening and strengthening. You’re actually not going to get significant strengthening or stiffening unless the link exceeds the critical length sometimes by quite a lot but the expression for the critical length is given here if Sigma F times D over two times tau sub C here Sigma F is the fibers ultimate tensile strength. D is the fiber diameter and Towson. C is the shear strength with a fiber matrix interface. So for example for fiber fiberglass a common fiber length greater than 15 millimeters is needed and typical is one millimeter might be for the critical length for the longer fibers.
The stress is transferred from the matrix more efficiently and say you have a stronger material so for a long thin fiber where that length is much greater than the critical length. Then you have a high fiber efficiency whereas if it’s less than a critical length then the efficiency of the fiber is much lower and it acts kind of more like a particle composite materials journals, journals on composite materials when it’s less than the critical length now when you place the fiber under longitudinal loading for a continuous fiber for example. That means that it’s a very long fiber and being the access of the orientation. The fibers called the longitudinal axis. When you place that under that you can get significant strengthening with your material the expression for quantifying what the elastic modulus is is shown here. E is the elastic modulus and Reese answer-there volume fraction so if the composite materials journals, journals on composite materials material when it’s under longitudinal is east and Cl that’s the elastic modulus. When the composite materials journals, journals on composite materials fiber is under it being loaded longitudinally and that’s equal to e sub. M times V sub M plus E Afton’s V sub X here F stands for the fiber and M stands for the matrix when flouted transfers. The fiber is carrying much less of the load so the strengthening in the transverse direction isn’t very much. It’s actually a comparable expression to what the lower bound for a particle in such. We went over later. And that’s shown here for translate transverse loading you have. 1 over e sub. CT t he R stands for transverse is equal to V M over m plus V s over es. Now you can estimate what the elastic modulus for a composite materials journals, journals on composite materials for discontinuous fibres are and this is valid when the fiber length is less than say 30 times the critical links or fifteen. Sigma FZ or cha subsea. In that case the expression looks like this ec50 right here. E is the elastic modulus again. C stands for composite materials journals, journals on composite materials and D stands for discontinuous is equal to e sub M V sub M plus K e FZ f K is actually an efficiency factor that ranges between 0 & 1.
The value is 1 when the fibers are all aligned and parallel to the longitudinal direction and K is equal to 0 when it’s aligned and perpendicular if it’s random in two dimensions K is often 3/8 and if it’s random in three dimensions k is often. One-fifth roughly this is an expression for the tensile strength for discontinuous fibres the tensile strength here is given by. Sigma when the length is greater than the critical length then Sigma star. C sub D is equal to Sigma F star times V F where the F is the volume fraction and Sigma F is the tensile strength of the fiber and then we have that times 1 minus LC where else use the critical length over to L where L is the actual length plus Sigma m prime times 1 minus VF. Now here when. L is less than a critical link Sigma sub. C D star is equal to L times L sub C over D times VF plus Sigma M prime times 1 minus VF. Now here the on D stands for diameter of course L stands for the length tau sub C is going to be the smaller of either the fiber matrix bond strength or the matrix shear a yield strength and if I didn’t say before the Sigma M. Prime is to stress in a matrix in the composite materials journals, journals on composite materials sails. There’s a few videos to actually that. I’ve posted on composite materials journals, journals on composite materials production materials and I really encourage you to watch it because it shows you what’s happening inside the factoring that’s really pretty interesting. But one of the more common production methods for composites materials journals, journals on composite materials is called pull trousias that’s when continuous fibers are pulled through a resin tank to impregnate the fibers with a thermosetting resin. And then those impregnated fibers pass through a steel dye that preforms it to the desired shape. And then the preform stock passes through a curing die that’s precision machined to impart the final shape and also heated to initiate the curing of the resin matrix. Now it’s actually pretty cool-looking when you watch the video still let my rather dull recitation of the facts.
Turn you off from watching it. Another common composite materials journals, journals on composite materials production method is called filament winding and that’s when continuous reinforcing fibers are accurately positioned in the predetermined pattern to form a hollow. Usually a cylindrical shape. And the fibers are fed through a resin bath to impregnate them with the thermosetting resin and then the impregnated fibers are continuously wound usually automatically onto a mandrel and then after a number of layers are added. Curing is carried out either in an oven or at room temperature and then they remove the mandrel to give the final product and the animation of that in the video that I post. This is really neat to watch. Finally you’re probably pretty familiar with structural composites materials journals, journals on composite materials . You’ve probably seen them around your house. They usually come in two broad types and those are laminates which are stacked in. Bondo’s fiber reinforced sheets. Sometimes they have a stacking sequence that gets discussed on the five carbon fiber for aircraft. Use video that. I’ve discussed why they choose the second sequences they do but a really common stacking sequence is to orient so the fibers are oriented this way and one layer and then perpendicular to that in the next layer and that provides them with increased tensile strength in either direction. They also have a more balanced in-plane stiffness and they don’t have that tendency to kind of curl up when they heat or cool that you might otherwise have you’ve probably seen sandwich panels and ceiling tiles. That’s a really common place to see them. And that’s when you have a honeycomb core between two facing sheets and the benefits are that they have a low density and they have a very large bending stiffness so to summarize. There’s a lot of benefits to compile. You can increase your toughness. You can increase your elastic modulus while decreasing your density of the material and you can increase your resistance to creep which strengthens their performance over time so I hope you enjoyed that and be sure to watch all those extra videos that are suitable.
Oh for more information base a lot.
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