Appendix C Sample Laboratory Report Lamina Tensile Response The lamina tensile response of a carbon-fiber,epoxy-matrix composite was examined experimentally to establish the intrinsic mechanical properties. The test specimen geometries were chosen according to the outline presented in Chapter 5,in accordance with ASTM standards.The specimens were loaded to failure in a tensile testing machine utilizing serrated wedge grips. Average test results and standard deviations were as follows: Elastic modulus in the fiber direction E1=126±2GPa Elastic modulus transverse to the fiber direction E2=10.2±0.4GPa Poisson's ratios:Major v2=0.30±0.01 Minor V2a-0.024 Ultimate tensile stress in the fiber direction XT=2037±85MPa Ultimate tensile stress in the transverse direction Xg-53±8MPa Ultimate tensile strain in the fiber direction e=0.015 Ultimate tensile strain in the transverse direction e1-0.0057 Procedure The procedure for this experiment is detailed in Chapter 5.Briefly,unidirec- tional panels were configured for achieving test specimens with 0 and 900 orientation as shown in Appendix B.After the edges of the panels were trimmed,tabs made from a glass-fabric epoxy laminate were adhesively bonded to both surfaces at two opposite edges of the panels.Four specimens of each orientation were machined to the appropriate widths using proce- dures detailed in Chapter 4.The 0 specimens were nominally 12.7 mm wide, whereas the 90 specimens were 25.4 mm wide.The 0 specimens were 8 plies thick,whereas the 90 specimens were 16 plies thick.To establish the axial stiffness(E),Poisson's ratio (v2),and the overall stress-strain response of the 0 specimens,a bidirectional(0/90)strain gage rosette was bonded at the geometric center on one surface of each specimen.In addition,an axial gage was bonded on the opposite surface of the specimen.For the 90 ©2003 by CRC Press LLC
Appendix C Sample Laboratory Report Lamina Tensile Response The lamina tensile response of a carbon–fiber, epoxy–matrix composite was examined experimentally to establish the intrinsic mechanical properties. The test specimen geometries were chosen according to the outline presented in Chapter 5, in accordance with ASTM standards. The specimens were loaded to failure in a tensile testing machine utilizing serrated wedge grips. Average test results and standard deviations were as follows: Procedure The procedure for this experiment is detailed in Chapter 5. Briefly, unidirectional panels were configured for achieving test specimens with 0 and 90° orientation as shown in Appendix B. After the edges of the panels were trimmed, tabs made from a glass–fabric epoxy laminate were adhesively bonded to both surfaces at two opposite edges of the panels. Four specimens of each orientation were machined to the appropriate widths using procedures detailed in Chapter 4. The 0° specimens were nominally 12.7 mm wide, whereas the 90° specimens were 25.4 mm wide. The 0° specimens were 8 plies thick, whereas the 90° specimens were 16 plies thick. To establish the axial stiffness (E1), Poisson’s ratio (ν12), and the overall stress–strain response of the 0° specimens, a bidirectional (0°/90°) strain gage rosette was bonded at the geometric center on one surface of each specimen. In addition, an axial gage was bonded on the opposite surface of the specimen. For the 90° Elastic modulus in the fiber direction E1 = 126 ± 2 GPa Elastic modulus transverse to the fiber direction E2 = 10.2 ± 0.4 GPa Poisson’s ratios: Major ν12 = 0.30 ± 0.01 Minor ν21 = 0.024 Ultimate tensile stress in the fiber direction X 1 T = 2037 ± 85 MPa Ultimate tensile stress in the transverse direction X 2 T = 53 ± 8 MPa Ultimate tensile strain in the fiber direction e 1 T = 0.015 Ultimate tensile strain in the transverse direction e 2 T = 0.0057 TX001_AppC_Frame Page 227 Saturday, September 21, 2002 5:14 AM © 2003 by CRC Press LLC
specimens,a single-element strain gage oriented along the length of the specimen was bonded to each surface of the specimen in the gage section to determine the axial stress-strain response.No strain gages transverse to the specimen loading axis were used because the minor Poisson's ratio(v2) may be determined from E,E2,and vi2.Each specimen was tested in a general-purpose testing machine at a crosshead rate of 2 mm/min.Specimen load and strains were sampled throughout the test using a PC-driven data acquisition system.The specimens were loaded to failure. Specimen Dimensions Specimen cross-sectional dimensions were recorded as follows: Specimen Orientation(deg)Width(w)(mm) Thickness (t)(mm) 1 0 12.78 1.067 3 0 12.78 1.067 3 0 12.65 1.067 0 12.75 1.067 90 25.40 2.184 6 90 25.35 2.185 7 90 25.45 2.134 8 90 25.53 2.236 Stress-Strain Data The load readings were converted to axial stress readings using the cross- sectional dimensions reported above.Examples of stress and strain data recorded using the data acquisition system are tabulated below. Stress-Strain Data for Specimen 2 ([0]s)(Reduced Set from Original Record) The last two columns are strain readings from the same strain gage rosette. C:(MPa) E(ustrain) E(ustrain) -e2(ustrain) 0 0 10 0 36 310 320 120 72 590 600 200 108 860 870 280 144 1,140 1160 340 180 1,420 1440 420 252 2,010 2,000 570 395 3,050 3,030 880 647 4,900 4850 1380 1.006 7,490 7,430 2.040 1,294 9,470 9.420 2540 1,617 11,640 11590 3,070 1,9772 14,060 13.990 3,610 a Ultimate stress. ©2003 by CRC Press LLC
specimens, a single-element strain gage oriented along the length of the specimen was bonded to each surface of the specimen in the gage section to determine the axial stress–strain response. No strain gages transverse to the specimen loading axis were used because the minor Poisson’s ratio (ν21) may be determined from E1, E2, and ν12. Each specimen was tested in a general-purpose testing machine at a crosshead rate of 2 mm/min. Specimen load and strains were sampled throughout the test using a PC-driven data acquisition system. The specimens were loaded to failure. Specimen Dimensions Specimen cross-sectional dimensions were recorded as follows: Stress–Strain Data The load readings were converted to axial stress readings using the crosssectional dimensions reported above. Examples of stress and strain data recorded using the data acquisition system are tabulated below. Specimen Orientation (deg) Width (w) (mm) Thickness (t) (mm) 1 0 12.78 1.067 2 0 12.78 1.067 3 0 12.65 1.067 4 0 12.75 1.067 5 90 25.40 2.184 6 90 25.35 2.185 7 90 25.45 2.134 8 90 25.53 2.236 Stress-Strain Data for Specimen 2 ([0]8) (Reduced Set from Original Record) The last two columns are strain readings from the same strain gage rosette. σ1 (MPa) ε1 (µstrain) ε1 (µstrain) –ε2 (µstrain) 0 0 10 0 36 310 320 120 72 590 600 200 108 860 870 280 144 1,140 1,160 340 180 1,420 1,440 420 252 2,010 2,000 570 395 3,050 3,030 880 647 4,900 4,850 1,380 1,006 7,490 7,430 2,040 1,294 9,470 9,420 2,540 1,617 11,640 11,590 3,070 1,977a 14,060 13,990 3,610 a Ultimate stress. TX001_AppC_Frame Page 228 Saturday, September 21, 2002 5:14 AM © 2003 by CRC Press LLC
Stress-Strain Data for Specimen 6([90]16) (Reduced Set from Original Record) G2 (MPa) E2(ustrain) 2(ustrain) 0 0 1.77 180 200 3.54 350 380 5.31 520 550 10.6 1040 1120 17.7 1750 1860 23.0 2290 2410 30.1 2990 3130 35.4 3520 3690 40.7 4120 4330 49.6 5050 5280 60.2 6220 6510 63. 6580 6879 Ultimate stress. Test Results Test results for three representative 0 test specimens are presented in graph- ical form in Figures C.1-C.3.The linear response region in the fiber direction is bounded by a strain of about 0.004.It is noteworthy that the stress-strain response exhibits strain hardening characteristics-a reflection of the strain hardening behavior of carbon fibers.Results for three representative 900 specimens are shown in Figures C.4-C.6.Here only a modest nonlinearity in the stress-strain response is observed.The strain softening is due to the nonlinear response of the epoxy matrix. Reduced Data The mechanical properties were reduced from the measured data using procedures and equations provided in Chapter 5.The following equations were employed: (C.1) E1 2s (C.2) E XT=G (C.3) 59 (C.4) E2 X=o2 (C.5) ©2003 by CRC Press LLC
Test Results Test results for three representative 0° test specimens are presented in graphical form in Figures C.1–C.3. The linear response region in the fiber direction is bounded by a strain of about 0.004. It is noteworthy that the stress–strain response exhibits strain hardening characteristics — a reflection of the strain hardening behavior of carbon fibers. Results for three representative 90° specimens are shown in Figures C.4–C.6. Here only a modest nonlinearity in the stress–strain response is observed. The strain softening is due to the nonlinear response of the epoxy matrix. Reduced Data The mechanical properties were reduced from the measured data using procedures and equations provided in Chapter 5. The following equations were employed: (C.1) (C.2) (C.3) (C.4) (C.5) Stress-Strain Data for Specimen 6 ([90]16) (Reduced Set from Original Record) σ2 (MPa) ε2 (µstrain) ε2 (µstrain) 00 0 1.77 180 200 3.54 350 380 5.31 520 550 10.6 1040 1120 17.7 1750 1860 23.0 2290 2410 30.1 2990 3130 35.4 3520 3690 40.7 4120 4330 49.6 5050 5280 60.2 6220 6510 63.4a 6580 6879 a Ultimate stress. E1 1 1 = σ ε υ ε ε 12 2 1 = − XT ult 1 1 = σ E2 2 2 = σ ε XT ult 2 2 = σ TX001_AppC_Frame Page 229 Saturday, September 21, 2002 5:14 AM © 2003 by CRC Press LLC
Carbon/Epoxy,[0]a 2000 -2 1500 00000 1000 500 0000000 0 ,2 .4 .681.0 1.2 1.4 76 Strain, FIGURE C.1 Stress-strain results for specimen 1(0). Carbon/Epoxy,[0]8 2000 -82 E1 1500 1000 500 0 6 .81.0 1.2 1.4 1.6 Strain,% FIGURE C.2 Stress-strain results for specimen 2(0). Carbon/Epoxy,[0] -82 E1 2000 1500 1000 500 0 .4 .6.81.0 1.2 1.4 1.6 Strain,% FIGURE C.3 Stress-strain results for specimen 3(0). ©2003 by CRC Press LLC
FIGURE C.1 Stress–strain results for specimen 1 (0°). FIGURE C.2 Stress–strain results for specimen 2 (0°). FIGURE C.3 Stress–strain results for specimen 3 (0°). TX001_AppC_Frame Page 230 Saturday, September 21, 2002 5:14 AM © 2003 by CRC Press LLC
Carbon/Epoxy,[9011s o 50 40 30 20 10 0 .2 .3.4 .5 .6 ,7 ,8 Strain (2),% FIGURE C.4 Stress-strain results for specimen 5(90). Carbon/Epoxy,[90]1 60 50 40 30 20 10 0 2 3 .4.5 .6 7 .8 Strain (), FIGURE C.5 Stress-strain results for specimen 6(90). 50 Carbon/Epoxy,[9011s 40 00 0 生四 0000-00-0-0-0000-0-0-000-0-00 20 10 0 1 2 3 5 .6 Strain (2)% FIGURE C.6 Stress-strain results for specimen 7(90). ©2003 by CRC Press LLC
FIGURE C.4 Stress–strain results for specimen 5 (90°). FIGURE C.5 Stress–strain results for specimen 6 (90°). FIGURE C.6 Stress–strain results for specimen 7 (90°). TX001_AppC_Frame Page 231 Saturday, September 21, 2002 5:14 AM © 2003 by CRC Press LLC
where o,and o,refer to the load per unit cross-sectional area(o=P/(wt)) for the 0 and 90 tests,respectively.Note that it was not possible to evaluate experimentally the minor Poisson's ratio,va,because the 90 specimens were not instrumented with a transversely oriented strain gage.The reduced data are summarized below. E(GPa) Ve X (MPa) e E2(GPa) X (MPa) e 128 0.295 2034 0.015 9.92 54.5 0.0056 127 0.292 1800 0.013 9.79 63.4 0.0067 124 0.299 2158 0.016 10.5 45.6 0.0046 125 0.319 1979 0.014 10.4 48.3 0.0049 Avg. 126 0.301 1993 0.015 10.2 53.0 0.0055 STD 2 0.012 149 0.001 0.4 7.9 0.0010 STD standard deviation. Using the reciprocal relations between the elastic moduli and Poisson's ratios given in Chapter 2,the minor Poisson's ratio was determined as V21=V12E2/E1=0.301×10.2/126=0.024 Uncertainty Analysis An uncertainty analysis was performed to estimate the possible scatter range in the mechanical properties as a result of uncertainties in the primary measurements of force,strain,and specimen dimensions.Procedures for such estimation are outlined in the text by Holman and Gajda [1].Here,we will perform a simple,conservative propagation of error analysis [1]on the governing Equations(C.1-C.5)used for data reduction and property deter- mination.Such an analysis yields =g+++訇 i=1,2 (C.6) 告+告 (C.7) =x[智++ i=1,2 (C.8) Consider the uncertainties in measuring the load(P),strain(E),and dimen- sions (w and t): AP=±10N △e=±5×106 2003 by CRC Press LLC
where σ1 and σ2 refer to the load per unit cross-sectional area (σ = P/(wt)) for the 0 and 90° tests, respectively. Note that it was not possible to evaluate experimentally the minor Poisson’s ratio, ν21, because the 90° specimens were not instrumented with a transversely oriented strain gage. The reduced data are summarized below. Using the reciprocal relations between the elastic moduli and Poisson’s ratios given in Chapter 2, the minor Poisson’s ratio was determined as ν21 = ν12E2/E1 = 0.301 × 10.2/126 = 0.024 Uncertainty Analysis An uncertainty analysis was performed to estimate the possible scatter range in the mechanical properties as a result of uncertainties in the primary measurements of force, strain, and specimen dimensions. Procedures for such estimation are outlined in the text by Holman and Gajda [1]. Here, we will perform a simple, conservative propagation of error analysis [1] on the governing Equations (C.1–C.5) used for data reduction and property determination. Such an analysis yields (C.6) (C.7) (C.8) Consider the uncertainties in measuring the load (P), strain (ε), and dimensions (w and t): ∆P = ±10N ∆ε = ±5 × 10–6 E1 (GPa) ν12 X1 T (MPa) e 1 T E2 (GPa) X2 T (MPa) e 2 T 128 0.295 2034 0.015 9.92 54.5 0.0056 127 0.292 1800 0.013 9.79 63.4 0.0067 124 0.299 2158 0.016 10.5 45.6 0.0046 125 0.319 1979 0.014 10.4 48.3 0.0049 Avg. 126 0.301 1993 0.015 10.2 53.0 0.0055 STDa 2 0.012 149 0.001 0.4 7.9 0.0010 a STD = standard deviation. ∆ ∆ ∆ ∆∆ E E P P w w t t i i i = + ++ = ε ε 1 2, ∆ ∆ ∆ υ υ ε ε ε ε 12 12 1 1 2 2 = + ∆ ∆∆ ∆ X X P P w w t t i i T i T = ++ = 1 2, TX001_AppC_Frame Page 232 Saturday, September 21, 2002 5:14 AM © 2003 by CRC Press LLC
△w=±0.025mm △t=±0.025mm With the above uncertainties in the load and strain data and in the cross- sectional dimensions,load and strain values were inserted into Equations (C.6)-(C.8)to yield the uncertainties in the reduced mechanical properties. When considering uncertainties in the elastic moduli(E)and Poisson's ratio(v12),the load and strains in the middle of the linear response region (Figures C.1-C.6)were used.For uncertainty analysis of the strengths (XT),the ultimate loads were used.The calculations yield the following uncertainties: △E1=3.2GPa △V12=0.002 AXT =52 MPa △E2=0.3GPa △X】=1.0MPa The uncertainties are all below 4%of the corresponding average values,which indicates that the measuring accuracy was reasonable.For several of the mechanical properties the standard deviation exceeds the above-estimated uncertainties,which indicates that the variability of the material properties contributes to the scatter. Micromechanics Predictions It is useful to compare the measured properties to those predicted by the micromechanics analyses discussed in Chapter 2.Previous laboratory experi- ments using an AS4/3501-6 carbon/epoxy composite gave a fiber volume fraction of 0.55(see Chapter 3).Application of the micromechanics relations for E1,Vi2,and E2 given in Chapter 2,i.e.,Equations (2.25a),(2.25c),and (2.26),together with the following data for AS4 carbon fibers and 3501-6 epoxy obtained from References [2-4]: Fiber Data [2,3] Matrix Data [3,4] Axial modulus (EL),235 GPa Young's modulus (E),4.28 GPa Transverse modulus (E),13.8 GPa Poisson's ratio (v),0.35 Axial Poisson's ratio (Vr),0.20 ©2003 by CRC Press LLC
∆w = ±0.025 mm ∆t = ±0.025 mm With the above uncertainties in the load and strain data and in the crosssectional dimensions, load and strain values were inserted into Equations (C.6)-(C.8) to yield the uncertainties in the reduced mechanical properties. When considering uncertainties in the elastic moduli (Ei ) and Poisson’s ratio (ν12), the load and strains in the middle of the linear response region (Figures C.1–C.6) were used. For uncertainty analysis of the strengths (Xi T), the ultimate loads were used. The calculations yield the following uncertainties: ∆E1 = 3.2 GPa ∆ν12 = 0.002 ∆X1 T = 52 MPa ∆E2 = 0.3 GPa ∆X2 T = 1.0 MPa The uncertainties are all below 4% of the corresponding average values, which indicates that the measuring accuracy was reasonable. For several of the mechanical properties the standard deviation exceeds the above-estimated uncertainties, which indicates that the variability of the material properties contributes to the scatter. Micromechanics Predictions It is useful to compare the measured properties to those predicted by the micromechanics analyses discussed in Chapter 2. Previous laboratory experiments using an AS4/3501-6 carbon/epoxy composite gave a fiber volume fraction of 0.55 (see Chapter 3). Application of the micromechanics relations for E1, ν12, and E2 given in Chapter 2, i.e., Equations (2.25a), (2.25c), and (2.26), together with the following data for AS4 carbon fibers and 3501-6 epoxy obtained from References [2–4]: Fiber Data [2,3] Matrix Data [3,4] Axial modulus (EL), 235 GPa Transverse modulus (ET), 13.8 GPa Axial Poisson’s ratio (νLT), 0.20 Young’s modulus (E), 4.28 GPa Poisson’s ratio (ν), 0.35 TX001_AppC_Frame Page 233 Saturday, September 21, 2002 5:14 AM © 2003 by CRC Press LLC
yields the following estimate of the mechanical properties of the composite E=131 GPa V12=0.27 E2=8.3 GPa The estimated properties agree reasonably well with the measured data.The differences may be due to variations in fiber volume fraction. References 1.J.P.Holman and W.J.Gajda,Jr.,Experimental Methods for Engineers,5th ed., McGraw-Hill,New York,1993. 2.Product Data,Number 841-4,Hercules Inc.,Wilmington,DE,1987. 3.J.Aboudi,Mechanics of Composite Materials-A Unified Micromechanical Approach, Studies in Applied Mechanics-29,Elsevier,Amsterdam,1991. 4.N.J.Johnston,T.W.Towell,and P.M.Hergenrother,Physical and mechanical properties of high-performance thermoplastic polymers and their composite materials,in Thermoplastic Composite Materials,L.A.Carlsson,ed.,Elsevier, Amsterdam,1991,pp.27-71. ©2003 by CRC Press LLC
yields the following estimate of the mechanical properties of the composite E1 = 131 GPa ν12 = 0.27 E2 = 8.3 GPa The estimated properties agree reasonably well with the measured data. The differences may be due to variations in fiber volume fraction. References 1. J.P. Holman and W.J. Gajda, Jr., Experimental Methods for Engineers, 5th ed., McGraw-Hill, New York, 1993. 2. Product Data, Number 841-4, Hercules Inc., Wilmington, DE, 1987. 3. J. Aboudi, Mechanics of Composite Materials — A Unified Micromechanical Approach, Studies in Applied Mechanics - 29, Elsevier, Amsterdam, 1991. 4. N.J. Johnston, T.W. Towell, and P.M. Hergenrother, Physical and mechanical properties of high-performance thermoplastic polymers and their composite materials, in Thermoplastic Composite Materials, L.A. Carlsson, ed., Elsevier, Amsterdam, 1991, pp. 27–71. TX001_AppC_Frame Page 234 Saturday, September 21, 2002 5:14 AM © 2003 by CRC Press LLC
