Lecture 37

Hello friends, welcome to the next lecture in the lecture series on testing in furlough mechanics. We have discussed in detail about the tension test, about the compression test in the last two lectures. I will talk about testing for bending in this lecture. This is course basics of mechanical engineering 1, which is co taught by professor Ram Kumar and Dr. Amandeep Singh Oberoi. I am Amandeep. Here, let us try to see first, what is bending testing? Bending testing is a mechanical test used to evaluate the behavior of materials under bending loads. So, this test measures the materials flexural strength, flexural modulus and resistance to deformation. So, that is why it is also known as flexural testing. It is particularly useful for assessing materials that are frequently used in structural applications. It could be metals, it could be plastics, it could be ceramics or even composites. We will talk about how this test is conducted. This is a specimen holding area. Why bending test is important? First point is for structural integrity. It ensures materials can withstand bending loads without failure, critical for safe and reliable structures. For design optimization, it helps to select materials with suitable strength and stiffness, optimizing designs for efficiency. Safety assurance, it ensures materials meet safety standards, reducing risk of structural failures. Now, let us now try to see the procedure for bending testing. First step is specimen preparation. Standardized dimensions again based upon certain standards ASTM or ISO standards are there based upon which the specimens are majorly here rectangular. It could be cylindrical depending upon the test that we are conducting. This is a rectangular specimen. It could be a cylindrical specimen. The demonstration that I will show you in the virtual environment would be a specimen that is a round shape that is a cylindrical specimen would be there. Then we have surface finish. Surface finish of the specimen should be smooth and free from any defects or irregularities so that it does not introduce any stress concentrations and does not affect the test results. So, there is a YouTube video. I will show you the video. Let me go through the procedure first. Mounting the specimen, there is a support span. So, it could be mid span or it could be one by third span when I am talking about the 3 point test or 3 point bending test. Specimen is placed on 2 supports with a specified span length between them. The span length is usually determined based on the dimensions of the specimen and testing standard being followed. So, it depends whether the specimen that we are selected for the testing is very thin or is it very solid and thick one. So, if it is a heavy specimen, the span length could be wide. If it is a small specimen, span length could be smaller. So, there are generally 2 configurations of loading. First is 3 point bending test. A single load is applied at the midpoint of the specimen between the supports. For instance, it is something like this. This is our specimen and a single load is applied here. So, this is called as 3 point. This is 3 point bending test. Then comes a 4 point bending test. 2 equal loads are applied at 2 points equidistant from the supports. So, here what we have specimen is there. It could be it is a length here and load is applied at 2 equidistant. So, this is 4 point bending test. We will go through the simulation video as well. Application of load is the next step. Controlled loading rate, the load is applied at a constant phase specified by the testing standard. The rate is controlled by the cross head speed of the testing machine. Generally, it is universal testing machine that is used here. Testing machine records the applied load and corresponding deflection that is bending of the specimen continuously. Then, we collect the data. That is data collection becomes the next step where load deflection curve is plotted. Recorded data is used to generate a load deflection curve showing the relationship between applied load and specimen's deflection. Then, we get the plastic and elastic grains. The plastic region is one that is non-linear part. Elastic is one that is linear part. This you know already. Then, what are the certain analysis that we get from this testing? First is the flexural strength. The maximum stress experienced by the material at its outermost fiber calculated using the load at failure, the span length and the specimen dimensions that is flexural strength. Then, comes flexural modulus. The slope of the linear portion of the deflection curve representing the material stiffness in bending that is flexural modulus. Then, comes failure characteristics such as how material fails whether by cracking, by breaking or yielding. This all is test here and is analyzed here. The setup is similar to what we had in the tensile and the compression test. Only the difference would be the loading system. Here, it will be different. I will show you that in the video. There are three dial gauges which are attached here. This is a three point loading. We have a load frame in a universal testing machine. We have a cross head that is movable so that the component applies load to the specimen. We have a load cell that measures the force. We have a bending fixture. This fixture depending upon three point or four point is designed differently. This includes supports and loading nodes. Then, we have the dial gauge or LVDT which measures the deflection of the specimen during the test, temperature control, environmental chamber. If it is a bending test that is under a specific temperature, we need to sometimes conduct a test at different temperatures. These temperatures could be high temperatures or may be very low temperatures up to may be minus 50 degrees or so. So, the temperature control system is used for testing materials at different temperatures to simulate real world conditions. Safety enclosures are always there when we have a temperature control system. Safety enclosures are used so that the fragments of the specimen does not harm the operator. Now, let us watch a video on how this test is conducted. Then, we will go through the simulation part of it. This is a video that is developed by the centrifugal system design. The engineers who have developed the virtual laboratory as well for the centrifugal system that I am using for the demonstration simulation as well. So, this is a video on the bending test. So, this is the experimental setup where the objective is to study the behavior of mild steel rods subjected to gradual increasing equal loads at one third span and to determine its mechanical properties. So, this is you can see a mild steel rod specimen is there that is a long specimen and here the length is 690. We first measure the initial diameter in 2 perpendicular dimensions. 2 perpendicular direction it is measured and average is taken. Then, we measure the length and then we mark the specimen for the middle point and the other 2 points to keep the span at mid span and one by third span. So, here l is 690 mm. So, one third loading points and the mid span where the dial gauge has to be placed this marking is needed. This is our bending fixture which has the setup so that the load is applied at the one third span. Now, dial gauges are also put down there exact at the points those were marked. So, there is one dial gauge at the mid span and 2 dial gauges are there at the one third spans. So, 3 dial gauges are all being set here. Now, we will adjust the dial gauge readings to 0 and we switch on the machine. Once this machine is switched on a gradual loading is done. You see the one third span and the mid span dial gauges are showing the reading and also there is a load that is being applied here. So, once the specimen is bent now we stop the experiment and we plot this total load versus dial indicator and we theoretical deflection and average dial reading is also plotted. So, that we see what is theoretical and the actual calculations. Then, we finally see the diameter model of elasticity stress at the point. All these are calculated and we try to finally get the bending modulus that is we try to get the flexural modulus of our specimen. This was the demonstration video. Now, let us try to see the simulation. This is a virtual laboratory setup where strength of materials experiments bending test on mild steel experiment is open. We can see the aim is given here to study the behavior of mild steel rods subjected to gradually increasing loads. It is gradually increasing loads, it is one third span to determine the mechanical properties. So, Curie part is completely given here that we have discussed in the previous lecture. It is the 3 point test and this is how we calculate the yield stress. How do we calculate the deflection with respect to A and all these parts you can further go through when you visit this website. So, let us try to see whether how ready are we to conduct the bending test. So, there are questions here for self evaluation. In bending test on mild steel dial indicators are used to the answers are find force applied, find value of stresses, record the value of deflection and none of these. We need to record the value of deflection. I will mark C as the answer. So, dial indicators will record the deflection. Then type of support used to fix the specimen in the bending test on mild steel is what kind of support is here. The support that is given is a roller support. When simply supported beam is subjected to center concentrated load W, then load W occurs at center with value of W L by 6 and W L R 3 by 58 into E I. Both maximum bending moment and maximum deflection occurs at center cross section. This is correct. So, B answer is correct here. Then the next question is as compared to uniaxial tension or compression, the strain energy stored in bending is only 1 by third. In simple bending theory, one of the assumption is that material of beam is isotropic. Assumption means that, so this means that elastic constants are same in all directions. Material is isotropic means in all directions, the elastic constants are same. Next question is pick up the correct assumption of theory of simple bending. Let us see what assumptions they have given. The resultant pull or thrust on transverse section of beam is 0. Material of beam is homogeneous and isotropic. Next point is transverse section of the beam remain clean before and after bending. All of them are correct. Yes, all of them are correct. Let us try to mark all of the above are correct. Rod is loaded in tension and pulled until it separates into 2 pieces. It is described as fracture rather than rupture. So, when it is separated into 2 pieces, they say it is fracture. No, we should say it is pulse. Let me submit the quiz 7 out of 7. All the questions are correct. Please go through the quiz time and again. If you do not mark any answer correct, you can may be re-answer that because multiple times we can submit the quiz. Then, we will go through simulation. In the simulation, let us go through the steps. Here is the apparatus that is used. So, this is the apparatus that is used. There is a fixture already that is here for the bending test. This is 3 point bending test fixture is there. These are all the parts of the universal testing machine. The cross head, the frame and everything is here. The first step is click on the rod and I measure the diameter of the rod using vernier caliper at 2 points. I move the moving jaw of the vernier caliper and measure the diameter here. So, diameter is 26. Again, we will measure it. I will click it and measure the diameter at another point. It is 25.2. So, average diameter is 25.6. Based upon the diameter that is given, I calculate the cross section area that is pi d square by 4. I calculate the moment of inertia that is pi d by 4 by 64. So, these are the values 514.72, 21072.18. Now, I need to measure the length of the specimen. Length of the specimen is measured using a scale. Then, I mark the pointers where the dial gauges are to be mounted or to be contacted with, so that the mid span and one third span is given. The length is 690 millimeters because the machine that we have here is having limitation to hold the specimen of 690 millimeters maximum. So, this length is marked here. Next step, that is step 4. We insert the specimen between the special two point loading set up with the roller support, which is being fixed on the lower cross head of the universal testing machine. Adjust all the dial gauges to 0. So, let us now fix the specimen here and mount the dial gauges. We set the dial gauges reading to 0 as we did it in tension. We did it in compression test as well. Then, we will start observing the loading here. The load is being applied. The total load dial gauge at mid span is changing here. This is dial gauge at mid span. Point A and point B are one third spans. So, both of the points are there. We take average of the two points and the loading is happening gradually here. These loads are equal load. You see 40, 80, 120, 160, 200. It is an increment of 40 kg of the load. This is an equal increment of the load. This was also set in the aim or objective of the experiment. Now, they say click on the red button to stop the loading process. We stop the loading. Yes, the data is now ready. We can download the data. You can see the data is downloaded into the excel sheet using this data. Now, we can plot our graphs. You see the material is bent here. This is the rod that is bent here. Now, we plot total load versus dial indicator reading. That is load versus deformation at mid span. We will see at this point some around till 640, the line is constant straight line. Then, only change comes. Then, only bending comes here. That is this point last deformation is here. Then, last deformation comes. We can also do the slope delta y, delta x. We can calculate. Yes, it is showing the yield point is here. Graphically, yield point has been gotten here. We can also calculate the yield point. Now, next step is average dial reading versus vertical deflection. Similarly, we will plot this line vertical deflection and average dial reading. Let us see the slope for this as well. Now, we need to calculate the moment of inertia about neutral axis stress at yield point and modulus of elasticity given the diameter of specimen, span of the beam, slope of deflection plot. I am not calculating it here because I am recording a video. Each time you will get a separate reading because this is a simulation. In simulation, there is a back hand where random numbers are there. Those numbers will be picked based upon the range of the different forces which are there for the specific material, for the specific diameter and this length of the material for the mild steel. Small changes will still come in realistic environments to simulate that realistic environment into this simulation, into this virtual environment. Each time you will get different numbers when you conduct or when you go through this simulation. You have to calculate these on the spot. That is how you put the values here. The formulas are also given here. It is moment of inertia about the neutral axis i is equal to pi into d power 4 by 64. Then, stress at yield point is m into y by i. Then, we have modulus of elasticity that is e is equal to 23 into l cube into slope into 9.81 by 1296 into i. These formulas are given. You just calculate the values, put it here and check whether right or not. These are the correct values that would come. These are the values that you have to be displayed. So, this is how the experiment is completed. Now, there are certain applications of the bending test as well. There are example applications which are given here. In the aerospace industry, bending testing is used to evaluate the flexural properties of composite material used in aircraft structures. So, bending test is a method employed by a genius to quantify the response of materials under direct beam loading. This is primarily used for materials that encompass as I told polymers, composites, even wood. Metals obviously are taken into test all the time. So, although commonly associated with brittleness, these materials are frequently rather ductile because bending we are talking about. We are not talking about how the material fracture. Material could also fracture. So, this enable their application in support structures such as skyscrapers, bridges, even big plastic objects like chairs, all of which encounter flexural stresses. So, in daily use, I am showing only example of the aircraft here. So, there are components or the parts of the aircraft such as wings, fuselage panels and other structural elements can withstand bending stresses encountered during flight. So, this contributes to the safety and performance of the aircraft. So, bending test is conducted to replicate a very realistic loading scenario. That is why we use three point and four point bending fixture which exerts stress through the distinct methods. So, based upon this specific criteria, material can undergo testing up to predetermined load or strain threshold or until the specimen experiences complete failure. The measured properties of this material are flexural stress, flexural strain, flexural modulus, flexural off-shell stress and all those are calculated using this test. All those are then determined using this test. So, I have shown you the application of the bending test and how the bending test is conducted. Now, I will go through the impact test in the next lecture and we will continue the series on the material testing. Thank you.