A2 _EN BUDAPEST UNIVERSITY OF TECHNOLOGY AND ECONOMICS FACULTY OF MECHANICAL ENGINEERING DEPARTMENT OF POLYMER ENGINEERING Flexural properties of polymers BENDING TEST OF CHECK THE VALIDITY OF NOTE ON WEBPAGE OF THE DEPARTMENT! WWW.PT.BME.HU
LOCATION OF THE PRACTICE CONTENTS 1. AIMS... 2. THEORETICAL BACKGROUND... 2.1. MEASURING CONDITIONS... 4 2.2. THE SPECIMEN... 6 2.. THE MECHANICAL PROPERTIES DETERMINED BY TENSILE TEST... 7. DESCRIBING OF PRACTICE, TASKS... 9 4. MACHINES... 9 5. RECOMMENDED LITERATURE... 9 MEASURING REPORT... 10 Bending Test of Polymers 2/10
1. Aims If you want to know the properties of a material, it is common to start to bend it. In some cases we found the one of them very inflexible, but the other - in same conditions and geometry - is soft. Some materials are rigid like glass, while others are deformable without any break. The aim of this practice is to study the behavior of polymeric materials by bending, the reason of these effects and its quantification. We use specimens made of different materials to present the quasistatic three point bending method, the characteristic mechanical properties, and the special effects of polymers, different from metals. 2. Theoretical background In bending test the specimen having standardized geometry is supported at it ends. The load is applied in the center of the specimen under standardized conditions (bending speed, temperature, humidity, etc.). The force is measured and registered during the deformation (bending). During the evaluation we calculate the flexural (bending) strength (proportional to the maximal load-bearing capacity), and the flexural modulus (proportional by the stiffness of material). The theoretical scheme and diagrams of bending, moment and shear of the test specimen are presented in Figure 1. deflection bending moment shear Figure 1. Three-point bending. Theoretical scheme, diagrams of deflection, moment and shear Bending Test of Polymers /10
The most important properties of polymers different from metals are: The moduli in compression and in tension are different, which causes the shifting of the neutral axis of bending from the center line The stress-deformation curve is not linear Big deformation even at relatively small load Low density The effect of the different compression- and tensile modulus can be compensated for by special equations. The nonlinearity of the bending characteristic can be considered by calculating of the bending modulus, and the big deformations before break by using the conventional bending stress. The relative low modulus (or the big deformability) is characteristic of polymers. That means the deflection of specimens (f) is sometimes larger than the validity of our classical calculation methods. If the deflection is too great, the pure bending state come to end, the shear forces become more important, the reaction forces are no more horizontal, the loaded and unloaded shape of specimen are increasingly different, etc. Practically if the f deflection is greater than 10% of the support distance (L) the Navier conditions become invalid, and we cannot use the regular calculation forms. We can solve the problem by limiting the deformation. We take the deflection in the measuring diagram into consideration only until our classical equations are valid. This is the conventional deflection, marked by f*, and its value is always 10% of the L support distance (f* =0.1. L). Therefore if the material breaks before f* we calculate the σ bh flexural strength, using the F t breaking force. But if the material is not braking until the conventional deflection (f*) is reached, we calculate the σ h flexural stress at conventional deflection instead, and use it to characterize the material. 2.1. Measuring conditions Bending speed: At higher bending speed the materials are more rigid. Their modulus and strength is bigger. Bending Test of Polymers 4/10
Measuring temperature: Polymers are very sensitive for relatively small differences in temperature. The change of temperature influences the stiffness, strength, and the bending characteristic. Under the glass transition temperature the polymers are rigid, in the rubbery state they are stiff (Figure 2.). Force [N] Deflection [mm] Figure 2. The effect of bending temperature using two different epoxy resins (EP-a and EP-b) 1: EP-a, 50 o C 2: EP-a, 2 o C : EP-b, 50 o C 4: EP-b, 2 o C Humidity: Some synthetic polymers are able to absorb enough water to change strongly their mechanical properties (PA, fiber-reinforced composites). The natural (wood, etc), natural based (starch, etc) and natural fiber reinforced polymers are also water sensitive. Water makes those materials softer, reduce their bending modulus and strength. Bending of composites: The behaviour of polymer composites differs strongly from that of the unreinforced materials. The most important factor is the fiber orientation. The fibers parallel with the load direction give the best bending properties; if they deviate from this direction the strength and modulus decrease (Figure.). The sandwich-systems are also important. Characteristic of them are the great increase of bending stiffness (D=IE, where I is the second moment, E is the modulus) that can be reached by a small excess material. Bending Test of Polymers 5/10
Force [N] Deflection [mm] Figure. The effect of orientation of polymer composites 2.2. The specimen The specimen is a simple rectangular beam, tested in arrangement presented in Figure 4. The most frequently used dimensions of specimens and testing equipment are presented in Table 1. Figure 4. Three-point bending 1: load probe, 2: support, : specimen, h: thickness of specimen, L: support distance Bending Test of Polymers 6/10
Standard Specimen size [mm] Support distance (L) [mm] Radii of supports and loading edge [mm] Length L t Width b Thickness h DIN 5452 120 15 10 100 10 1 ISO/R 178 80 10 4 64 5 2 Table 1. Standard sizes of specimen and equipment R 1 R 2 2.. The mechanical properties determined by tensile test The bending test is carried out using constant crosshead speed, so the deflection is increased uniformly. We register the force as a function of deflection. Flexural strength: Tthe σ bh flexural strength, namely the maximum stress at break, is calculated using Equation (1): M bh (1) K where σ bh the flexural strength, M is the maximum bending moment in the specimen, K is the crosssectional coefficient. Taking the moment: M and the cross-sectional coefficient: F L FL 2 2 4 2 bh K after simplifying the expression we have Equation (2), arising also in the EN ISO 6 178:2001 Standard: FL bh [MPa] (2) 2 2bh where F is the breaking force in Newton, L is the support distance in mm, b is the width of specimen in mm, h is the thickness of specimen in mm. Flexural stress at conventional deflection: If the specimen do not brake until the conventional deflection (0.1*L) we use the σ h flexural stress at conventional deflection instead of the flexural strength. The calculation is similar, but we use the bending force at conventional deflection instead of the breaking force. Bending Test of Polymers 7/10
Flexural modulus: By calculating E h flexural modulus our starting point is the differential equation of the neutral axis, which is in our case: M y 1 '' R IE where I is the second moment. Solving the equation gives Equation (4): () f FL (4) 48IE where f is the deflection. By regrouping this equation and substitute the we obtain Equation (5), which is the equation appearing in the standards: bl I second moment 12 1 L 4 bh E h F [MPa] (5) f where L is the support distance in mm, b is the width of specimen in mm, h is the thickness of specimen in mm, F/ f is the slope of the force-deflection curve. But generally this curve is not straight. We take this nonlinearity into consideration in the determination of f and F. In this practice we define the initial flexural modulus. We draw a line to the nearly linear starting section of the force-deflection curve. The initial flexural modulus is calculated using the slope of this line. The measuring of f and F are presented in Figure 5. Figure 5. Initial slope of the bending force-deflection diagram The standard test methods calculate the f and F values in two standardized points of the curve. In this case the modulus is the chord modulus between ε 1 =0.0005 and ε 2 =0.0025. Bending Test of Polymers 8/10
. Describing of the practice, tasks The aim of the practice is to measure three-point bending specimens made of different materials and methods, then calculate the characteristic strength and the flexural modulus. The course of measurements: 1. Flexural testing of different materials according to Figure 4. 2. Measure the initial slope of the diagram, measure the values of F and f. Fill the specimen data into the table of the measuring report: thickness (h), width (b), overall length (l), weight (m), density (ρ). 4. Determine the force at break or at conventional deflection. 5. Calculate the flexural modulus (E h ), the flexural strength (σ bh ), or the flexural stress at conventional deflection (σ h ). 6. Determine the relationship of different material properties and the density. 4. Machines ZWICK 05 UNIVERSAL TENSILE MACHINE Measuring range: 5 kn Crosshead speed: 0,0005-000 mm/min Figure 6. Three-point bending equipment 5. Recommended literature 1. EN ISO 178:2001 standard: Plastics- Determination of flexural properties (2001). 2. EN ISO 527:1998 standard: Fibre-reinforced plastics composites- Determination of flexural properties (1998). Bending Test of Polymers 9/10
MEASURING REPORT Name: Neptun code: Date: Leader s name: classification signature of practice leader 1. Dates Temperature:.. [ C] Humidity:.. [%] Support distance (L):.. [mm] Conventional deflection (f*):.. [mm] Specimen data Measured and calculated results Material σ h b l m ρ F f E bh h E/ρ or σ h MPa cm [mm] [mm] [mm] [g] [g/cm ] [N] [mm] [MPa] [MPa] g 1 2 4 5 6 7 8 9 10 11 12 h thickness, b width, l length, m mass, ρ density, E h modulus, σ bh or σ h strength Bending Test of Polymers 10/10