Z.M. Huang /Computers and Structures 80(2002)1177-1199 Table 2 Properties of Silenka E-glass 1200tex and MY750/HY917/DY063 epoxy UD lamina Properties Lamina Provided Predicted Provided Used Provided 45.6 Ex(gPa 16.2 13.45 3.35 3.35 30.8 30.8 124 0.278 0.2 0.35 0.35 GY),(MPa) (ar)2(MPa (aY)3(MPa 6.8 (OY)(MPa (aY)s(MP 56 (ay)(MP (ar),(MPa)a EEEEEE PPPPPPP (ET),(mPa)a .0882746 ET),(MPa) 80 2150 2092.8 9 74.8 8.8 aT(MPa GS(MP 77048 ElL.c (%)c 0.246 212(%y x1(×10-6°C) 9 x2(×10-O)264 2962000 4.9 13.558 880 02(MPa产 7.32 10.988 Fiber volume fraction: Vr=0.60: stress-free temperature: 120C; working temperature: 25C: bridging parameters used: B=0.45 and a assumed to be the same in both tension and compression b Longitudinal tension d transverse tension Transverse compression. In-plane shearing. Not for use in subsequent predictions. Predicted thermal residual stress, from stress-free temperature to working temperature back calculated based on the overall longitudinal re- ulus of the matrix at a specific loading range was spec- sponse of the composite, since in some cases the matrix ified as material may not sustain a full load share (i.e. to its maximum load carry ning capacit) when the composite is=(=),when()≤四≤(四) longitudinally loaded up to failure. The retrieved uni- axial stress-strain curve of each matrix was assumed to consist of eight linear segments. Hence, hardening mod- (ET)o=Em,oY)=0
back calculated based on the overall longitudinal response of the composite, since in some cases the matrix material may not sustain a full load share (i.e. to its maximum load carrying capacity) when the composite is longitudinally loaded up to failure. The retrieved uniaxial stress–strain curve of each matrix was assumed to consist of eight linear segments. Hence, hardening modulus of the matrix at a specific loading range was specified as Em T ¼ Em T i ; when rm Y i 6 rm e 6 rm Y iþ1; i ¼ 0; 1; ... ; 7; Em T 0 ¼ Em; rm Y 0 ¼ 0; ð11:1Þ Table 2 Properties of Silenka E-glass 1200tex and MY750/HY917/DY063 epoxy UD lamina Properties Lamina Fiber Resin Provided Predicted Provided Used Provided Used E11 (GPa) 45.6 45.74 74 74 3.35 3.35 E22 (GPa) 16.2 13.45 74 74 3.35 3.35 G12 (Gpa) 5.83 5.31 30.8 30.8 1.24 1.24 m12 0.278 0.26 0.2 0.2 0.35 0.35 ðrYÞ1 (MPa)a ––––– 32.6 ðrYÞ2 (MPa)a ––––– 39.9 ðrYÞ3 (MPa)a ––––– 46.8 ðrYÞ4 (MPa)a – – – – – 52 ðrYÞ5 (MPa)a ––––– 55.6 ðrYÞ6 (MPa)a – – – – – 58 ðrYÞ7 (MPa)a ––––– 60.1 ðrYÞ8 (MPa)a ––––– 62.0 ðETÞ1 (MPa)a – – – – – 1 698 ðETÞ2 (MPa)a – – – – – 1 387 ðETÞ3 (MPa)a – – – – – 91 8 ðETÞ4 (MPa)a – – – – – 542 ðETÞ5 (MPa)a – – – – – 31 7 ðETÞ6 (MPa)a – – – – – 244 ðETÞ7 (MPa)a – – – – – 1 86 rL u (MPa)b 1280 1280 2150 2092.8 80 60.9 rL u;c (MPa)c 800 800 1450 1311.8 120 74.8 rT u (MPa)d 40 78.8 – – – – rT u;c (MPa)e 145 145 – – – – rS u (MPa)f 73 90 – – – – e11 (%)b 2.807 2.820 – – 5 5.7704g e11;c (%)c 1.754 1.749 – – – – e22 (%)d 0.246 0.835 – – – – e22;c (%)e 1.2 2.918 – – – – 2e12 (%)f 4 9.875 – – – – a1ð 106/C) 8.6 6.46 4.9 4.9 58 58 a2ð 106/C) 26.4 21.67 4.9 4.9 58 58 r11 (MPa)h –0– 13.55g – 20.33g r22 (MPa)h –0– 7.32g – 10.98g r12 (MPa)h –0–0–0 Fiber volume fraction: Vf ¼ 0:60; stress-free temperature: 120 C; working temperature: 25 C; bridging parameters used: b ¼ 0:45 and a ¼ 0:35. a Assumed to be the same in both tension and compression. bLongitudinal tension. c Longitudinal compression. dTransverse tension. e Transverse compression. f In-plane shearing. g Not for use in subsequent predictions. h Predicted thermal residual stress, from stress-free temperature to working temperature. 1182 Z.-M. Huang / Computers andStructures 80 (2002) 1177–1199
Z-M. Huang Computers and Structures 80(2002)1177-1199 Table 3 Properties of graphite AS4 and 3501-6 UD lamina Properties Provided Predicted Provided Used Provided Used Eu(gPa) Ex(GPa 9.23 Gn(Gpa) 6.6 1567 0.256 GY),(MPa)y (ar)2(MP 4l.8 (aY)3(MPa) (OY)(MPa) (aY)s(MPa) 4.0 (ar),(MPa)a 12 GY)(mPa) (ET),(mPa)a 507 Er),(MPa)a 2530 2072 ET)(MPa) TTT 1950 3206.4 1480 2458.6 1164 (MPa) 659 MPar GS( (MPay 98.8 1420 2.5424 1.175 0.436 3.404 2a12(% -0.5 45 45 -22.238 (MPa) 02000 5533 9.063 Fiber volume fraction: Vr =0.60: stress-free temperature: 177C; working temperature: 25C: bridging parameters used: B=0.45 and Assumed to be the same in both tension and compression Longitudinal compression d transverse tension Transverse compression. subsequent predictions Predicted thermal residual stress, from stress-free temperature to working temperature and理=()y, when a≥(q) (11.2) that the predicted plastic strain at this stress level was equal to 0.02 CY/Em. The retrieved matrix plastic pa- The recovering was performed as follows. Starting from rameters of the four laminae are summarized in Tables the given elastic modulus, Em the remaining hardening 1-4, respectively moduli of the matrix were adjusted in such a way that It is evident that the most important parameters the predicted in-plane shear stress-shear strain curve the present modeling approach to the composite strength was as close to the provided one as possible. The yield are the ultimate strength data of the constituent ma- strength, a=(o), was determined using a condition terials. The tensile and compressive strengths of the
and Em T ¼ Em T 7; when rm e P rm Y 8: ð11:2Þ The recovering was performed as follows. Starting from the given elastic modulus, Em the remaining hardening moduli of the matrix were adjusted in such a way that the predicted in-plane shear stress–shear strain curve was as close to the provided one as possible. The yield strength, rm Y ðrm YÞ1, was determined using a condition that the predicted plastic strain at this stress level was equal to 0.02 rm Y=Em. The retrieved matrix plastic parameters of the four laminae are summarized in Tables 1–4, respectively. It is evident that the most important parameters in the present modeling approach to the composite strength are the ultimate strength data of the constituent materials. The tensile and compressive strengths of the Table 3 Properties of graphite AS4 and 3501-6 epoxy UD lamina Properties Lamina Fiber Resin Provided Predicted Provided Used Provided Used E11 (GPa) 126 136.7 225 225 4.2 4.2 E22 (GPa) 11 9.23 15 15 4.2 4.2 G12 (Gpa) 6.6 5.54 15 15 1.567 1.567 m12 0.28 0.256 0.2 0.2 0.34 0.34 ðrYÞ1 (MPa)a – – – –– 38.1 ðrYÞ2 (MPa)a – – – – – 41 .8 ðrYÞ3 (MPa)a – – – –– 46.1 ðrYÞ4 (MPa)a – – – –– 50.1 ðrYÞ5 (MPa)a – – – –– 54.0 ðrYÞ6 (MPa)a – – – –– 57.6 ðrYÞ7 (MPa)a – – – – – 61 .2 ðrYÞ8 (MPa)a – – – –– 64.6 ðETÞ1 (MPa)a – – – –– 2507 ðETÞ2 (MPa)a – – – –– 2530 ðETÞ3 (MPa)a – – – –– 2072 ðETÞ4 (MPa)a – – – – – 1 721 ðETÞ5 (MPa)a – – – – – 1 409 ðETÞ6 (MPa)a – – – – – 1 202 ðETÞ7 (MPa)a – – – – – 991 rL u (MPa)b 1950 1950 3350 3206.4 69 65.6 rL u;c (MPa)c 1480 1480 2500 2458.6 250 116.4 rT u (MPa)d 48 65.9 – – – – rT u;c (MPa)e 200 200 – – – – rS u (MPa)f 79 98.8 – – 50 – e11 (%)b 1.38 1.420 – – 1.7 2.5424g e11;c (%)c 1.175 1.084 – – – – e22 (%)d 0.436 0.792 – – – – e22;c (%)e 2.0 3.404 – – – – 2e12 (%)f 2 3.187 – – – – a1ð 106/C) 10.06 0.5 0.5 45 45 a2ð 106/C) 26 27.9 15 15 45 45 r11 (MPa)h –0– 22.23g – 33.35g r22 (MPa)h –0– 9.06g – 13.6g r12 (MPa)h – 0 – 0– 0 Fiber volume fraction: Vf ¼ 0:60; stress-free temperature: 177 C; working temperature: 25 C; bridging parameters used: b ¼ 0:45 and a ¼ 0:3. a Assumed to be the same in both tension and compression. bLongitudinal tension. c Longitudinal compression. dTransverse tension. e Transverse compression. f In-plane shearing. g Not for use in subsequent predictions. h Predicted thermal residual stress, from stress-free temperature to working temperature. Z.-M. Huang / Computers andStructures 80 (2002) 1177–1199 1183
Z-M. Huang / Computers and Structures 80(2002)1177-1199 Table 4 Properties of graphite T300 and bSL914C epoxy UD lamina Provided Predicted Provided Used Provided Used Ex(gPa 0.35 (ar)2(MPa (aY)3(MPa (OY)(MPa (aY)s(MP EEEEEE TTTTTT PPPPPPPP 1500 00 14994 l16.8 MPa)d aT(MPa GS(MP 81.2 1087 ElL.c (%)c 0.652 0.245 0.641 2c(%)° 1.818 212(%y 4.578 x1(×10-6/C) 0.06 -0.7 -0.7 554 02(MPa产 000 -7499 11243 Fiber volume fraction: Vr=0.60: stress-free temperature: 120C; working temperature: 25C: bridging parameters used: B=0.45 and a assumed to be the same in both tension and compression b Longitudinal tension ransverse tension Transverse compression. s Not for use in subsequent predictions. Predicted thermal residual stress, from stress-free temperature to working temperature constituents are retrieved from the ultimate strengths of(-570)MPa, a transverse tension of 35 MPa, a trans- the Ud laminae. The retrieval is accomplished by ap- plying the ultimate uniaxial loads to the respective Ud shearing of 72 MPa to the E-Glass 21 x K43 Gevetex lamina. The resulting largest and smallest maximum and and ly556/Ht907/DY063 epoxy Ud lamina with a fiber minimum stresses in the fiber and matrix materials are volume fraction of 0.62(see table 1), the calculated defined as their respective tensile and compressive maximum or minimum stresses in the fiber and matrix trengths. For example, when applying a longitudinal materials are: omax= 1804. 1 MPa and om.=56.5 MPa tension of 1140 MPa, a longitudinal compression of(corresponding to the longitudina ension). 0
constituents are retrieved from the ultimate strengths of the UD laminae. The retrieval is accomplished by applying the ultimate uniaxial loads to the respective UD lamina. The resulting largest and smallest maximum and minimum stresses in the fiber and matrix materials are defined as their respective tensile and compressive strengths. For example, when applying a longitudinal tension of 1140 MPa, a longitudinal compression of (570) MPa, a transverse tension of 35 MPa, a transverse compression of (114) MPa, and an in-plane shearing of 72 MPa to the E-Glass 21 K43 Gevetex and LY556/HT907/DY063 epoxy UD lamina with a fiber volume fraction of 0.62 (see Table 1), the calculated maximum or minimum stresses in the fiber and matrix materials are: rf max ¼ 1804:1MPa and rm max ¼ 56:5 MPa (corresponding to the longitudinal tension), rf min ¼ Table 4 Properties of graphite T300 and BSL914C epoxy UD lamina Properties Lamina Fiber Resin Provided Predicted Provided Used Provided Used E11 (GPa) 138 139.6 230 230 4.0 4.0 E22 (GPa) 11 9.09 15 15 4.0 4.0 G12 (Gpa) 5.5 5.04 15 15 1.481 1.481 m12 0.28 0.26 0.2 0.2 0.35 0.35 ðrYÞ1 (MPa)a – – – – – 41 .6 ðrYÞ2 (MPa)a – – – –– 49.6 ðrYÞ3 (MPa)a – – – –– 55.8 ðrYÞ4 (MPa)a – – – –– 59.9 ðrYÞ5 (MPa)a – – – –– 63.1 ðrYÞ6 (MPa)a – – – –– 66.3 ðrYÞ7 (MPa)a – – – –– 68.9 ðrYÞ8 (MPa)a – – – – – 71 .4 ðETÞ1 (MPa)a – – – – – 201 5 ðETÞ2 (MPa)a – – – – – 1 384 ðETÞ3 (MPa)a – – – – – 769 ðETÞ4 (MPa)a – – – – – 548 ðETÞ5 (MPa)a – – – – – 457 ðETÞ6 (MPa)a – – – – – 324 ðETÞ7 (MPa)a – – – – – 275 rL u (MPa)b 1500 1500 2500 2462.5 75 56.4 rL u;c (MPa)c 900 900 2000 1499.4 150 116.8 rT u (MPa)d 27 55.8 – – – – rT u;c (MPa)e 200 200 – – – – rS u (MPa)f 80 81.2 – – 70 – e11 (%)b 1.087 1.073 – – 4 5.4139g e11;c (%)c 0.652 0.645 – – – – e22 (%)d 0.245 0.641– – – – e22;c (%)e 1.818 6.891 – – – – 2e12 (%)f 4 4.578 – – – – a1ð 106/C) 1 0.06 0.7 0.7 55 55 a2ð 106/C) 26 29.6 12 12 55 55 r11 (MPa)h –0– 16.59g – 24.89g r22 (MPa)h –0– 7.49g – 11.24g r12 (MPa)h – 0 – 0– 0 Fiber volume fraction: Vf ¼ 0:60; stress-free temperature: 120 C; working temperature: 25 C; bridging parameters used: b ¼ 0:45 and a ¼ 0:35. a Assumed to be the same in both tension and compression. bLongitudinal tension. c Longitudinal compression. dTransverse tension. e Transverse compression. f In-plane shearing. g Not for use in subsequent predictions. h Predicted thermal residual stress, from stress-free temperature to working temperature. 1184 Z.-M. Huang / Computers andStructures 80 (2002) 1177–1199