Novel modified distribution functions of fiber length in fiber reinforced thermoplastics
Amongst the present prediction models of mechanical properties, the Weibull distribution has been introduced to describe the fiber length distribution. However, the Weibull distribution cannot capture the long tail decay, leading to underestimation of the fiber length factor (χ 2). For the first tim...
Ausführliche Beschreibung
Autor*in: |
Huang, Dayong [verfasserIn] |
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Sprache: |
Englisch |
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2019transfer abstract |
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Enthalten in: No title available - an international journal, Amsterdam [u.a.] |
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Übergeordnetes Werk: |
volume:182 ; year:2019 ; day:29 ; month:09 ; pages:0 |
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DOI / URN: |
10.1016/j.compscitech.2019.107749 |
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Katalog-ID: |
ELV047796693 |
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520 | |a Amongst the present prediction models of mechanical properties, the Weibull distribution has been introduced to describe the fiber length distribution. However, the Weibull distribution cannot capture the long tail decay, leading to underestimation of the fiber length factor (χ 2). For the first time, two novel modified distribution functions are proposed based on Erlang-2 distribution and Weibull distribution, respectively. The modified Erlang distribution is derived from introducing a shape parameter to capture the sharp peak better, whereas the modified Weibull distribution is developed by introducing a polynomial function instead of the exponential function to reduce the decay rate for the long fibers. The modified distribution functions are investigated by experimental data reported in literatures and the experimental data of GFRPA66 we obtained. The relationship between the shape parameters (α and β) and k can be described by a linear growth function when α >β, and the slope of α~k is larger than that of β~k. The scale parameters (λ, λ α and λ β ) can be considered as the linear growth function of l n. The relationship between the improvement in fiber length factor (Δ) and the improvement in number-average fiber length (δ) can be described by a fitting power function with an offset. In comparison to the Weibull distribution, the modified distribution functions improve more than 4% in χ 2. The modified Weibull distribution tends to capture the actual fiber length distribution for LFT, whereas the modified Erlang distribution captures that for SFT. | ||
520 | |a Amongst the present prediction models of mechanical properties, the Weibull distribution has been introduced to describe the fiber length distribution. However, the Weibull distribution cannot capture the long tail decay, leading to underestimation of the fiber length factor (χ 2). For the first time, two novel modified distribution functions are proposed based on Erlang-2 distribution and Weibull distribution, respectively. The modified Erlang distribution is derived from introducing a shape parameter to capture the sharp peak better, whereas the modified Weibull distribution is developed by introducing a polynomial function instead of the exponential function to reduce the decay rate for the long fibers. The modified distribution functions are investigated by experimental data reported in literatures and the experimental data of GFRPA66 we obtained. The relationship between the shape parameters (α and β) and k can be described by a linear growth function when α >β, and the slope of α~k is larger than that of β~k. The scale parameters (λ, λ α and λ β ) can be considered as the linear growth function of l n. The relationship between the improvement in fiber length factor (Δ) and the improvement in number-average fiber length (δ) can be described by a fitting power function with an offset. In comparison to the Weibull distribution, the modified distribution functions improve more than 4% in χ 2. The modified Weibull distribution tends to capture the actual fiber length distribution for LFT, whereas the modified Erlang distribution captures that for SFT. | ||
650 | 7 | |a Fiber length factor |2 Elsevier | |
650 | 7 | |a Fiber length distribution |2 Elsevier | |
650 | 7 | |a Weibull distribution |2 Elsevier | |
650 | 7 | |a Shape and scale parameters |2 Elsevier | |
700 | 1 | |a Zhao, Xianqiong |4 oth | |
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10.1016/j.compscitech.2019.107749 doi GBV00000000000738.pica (DE-627)ELV047796693 (ELSEVIER)S0266-3538(19)30622-0 DE-627 ger DE-627 rakwb eng Huang, Dayong verfasserin aut Novel modified distribution functions of fiber length in fiber reinforced thermoplastics 2019transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Amongst the present prediction models of mechanical properties, the Weibull distribution has been introduced to describe the fiber length distribution. However, the Weibull distribution cannot capture the long tail decay, leading to underestimation of the fiber length factor (χ 2). For the first time, two novel modified distribution functions are proposed based on Erlang-2 distribution and Weibull distribution, respectively. The modified Erlang distribution is derived from introducing a shape parameter to capture the sharp peak better, whereas the modified Weibull distribution is developed by introducing a polynomial function instead of the exponential function to reduce the decay rate for the long fibers. The modified distribution functions are investigated by experimental data reported in literatures and the experimental data of GFRPA66 we obtained. The relationship between the shape parameters (α and β) and k can be described by a linear growth function when α >β, and the slope of α~k is larger than that of β~k. The scale parameters (λ, λ α and λ β ) can be considered as the linear growth function of l n. The relationship between the improvement in fiber length factor (Δ) and the improvement in number-average fiber length (δ) can be described by a fitting power function with an offset. In comparison to the Weibull distribution, the modified distribution functions improve more than 4% in χ 2. The modified Weibull distribution tends to capture the actual fiber length distribution for LFT, whereas the modified Erlang distribution captures that for SFT. Amongst the present prediction models of mechanical properties, the Weibull distribution has been introduced to describe the fiber length distribution. However, the Weibull distribution cannot capture the long tail decay, leading to underestimation of the fiber length factor (χ 2). For the first time, two novel modified distribution functions are proposed based on Erlang-2 distribution and Weibull distribution, respectively. The modified Erlang distribution is derived from introducing a shape parameter to capture the sharp peak better, whereas the modified Weibull distribution is developed by introducing a polynomial function instead of the exponential function to reduce the decay rate for the long fibers. The modified distribution functions are investigated by experimental data reported in literatures and the experimental data of GFRPA66 we obtained. The relationship between the shape parameters (α and β) and k can be described by a linear growth function when α >β, and the slope of α~k is larger than that of β~k. The scale parameters (λ, λ α and λ β ) can be considered as the linear growth function of l n. The relationship between the improvement in fiber length factor (Δ) and the improvement in number-average fiber length (δ) can be described by a fitting power function with an offset. In comparison to the Weibull distribution, the modified distribution functions improve more than 4% in χ 2. The modified Weibull distribution tends to capture the actual fiber length distribution for LFT, whereas the modified Erlang distribution captures that for SFT. Fiber length factor Elsevier Fiber length distribution Elsevier Weibull distribution Elsevier Shape and scale parameters Elsevier Zhao, Xianqiong oth Enthalten in Elsevier No title available an international journal Amsterdam [u.a.] (DE-627)ELV013958402 nnns volume:182 year:2019 day:29 month:09 pages:0 https://doi.org/10.1016/j.compscitech.2019.107749 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U GBV_ILN_40 AR 182 2019 29 0929 0 |
spelling |
10.1016/j.compscitech.2019.107749 doi GBV00000000000738.pica (DE-627)ELV047796693 (ELSEVIER)S0266-3538(19)30622-0 DE-627 ger DE-627 rakwb eng Huang, Dayong verfasserin aut Novel modified distribution functions of fiber length in fiber reinforced thermoplastics 2019transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Amongst the present prediction models of mechanical properties, the Weibull distribution has been introduced to describe the fiber length distribution. However, the Weibull distribution cannot capture the long tail decay, leading to underestimation of the fiber length factor (χ 2). For the first time, two novel modified distribution functions are proposed based on Erlang-2 distribution and Weibull distribution, respectively. The modified Erlang distribution is derived from introducing a shape parameter to capture the sharp peak better, whereas the modified Weibull distribution is developed by introducing a polynomial function instead of the exponential function to reduce the decay rate for the long fibers. The modified distribution functions are investigated by experimental data reported in literatures and the experimental data of GFRPA66 we obtained. The relationship between the shape parameters (α and β) and k can be described by a linear growth function when α >β, and the slope of α~k is larger than that of β~k. The scale parameters (λ, λ α and λ β ) can be considered as the linear growth function of l n. The relationship between the improvement in fiber length factor (Δ) and the improvement in number-average fiber length (δ) can be described by a fitting power function with an offset. In comparison to the Weibull distribution, the modified distribution functions improve more than 4% in χ 2. The modified Weibull distribution tends to capture the actual fiber length distribution for LFT, whereas the modified Erlang distribution captures that for SFT. Amongst the present prediction models of mechanical properties, the Weibull distribution has been introduced to describe the fiber length distribution. However, the Weibull distribution cannot capture the long tail decay, leading to underestimation of the fiber length factor (χ 2). For the first time, two novel modified distribution functions are proposed based on Erlang-2 distribution and Weibull distribution, respectively. The modified Erlang distribution is derived from introducing a shape parameter to capture the sharp peak better, whereas the modified Weibull distribution is developed by introducing a polynomial function instead of the exponential function to reduce the decay rate for the long fibers. The modified distribution functions are investigated by experimental data reported in literatures and the experimental data of GFRPA66 we obtained. The relationship between the shape parameters (α and β) and k can be described by a linear growth function when α >β, and the slope of α~k is larger than that of β~k. The scale parameters (λ, λ α and λ β ) can be considered as the linear growth function of l n. The relationship between the improvement in fiber length factor (Δ) and the improvement in number-average fiber length (δ) can be described by a fitting power function with an offset. In comparison to the Weibull distribution, the modified distribution functions improve more than 4% in χ 2. The modified Weibull distribution tends to capture the actual fiber length distribution for LFT, whereas the modified Erlang distribution captures that for SFT. Fiber length factor Elsevier Fiber length distribution Elsevier Weibull distribution Elsevier Shape and scale parameters Elsevier Zhao, Xianqiong oth Enthalten in Elsevier No title available an international journal Amsterdam [u.a.] (DE-627)ELV013958402 nnns volume:182 year:2019 day:29 month:09 pages:0 https://doi.org/10.1016/j.compscitech.2019.107749 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U GBV_ILN_40 AR 182 2019 29 0929 0 |
allfields_unstemmed |
10.1016/j.compscitech.2019.107749 doi GBV00000000000738.pica (DE-627)ELV047796693 (ELSEVIER)S0266-3538(19)30622-0 DE-627 ger DE-627 rakwb eng Huang, Dayong verfasserin aut Novel modified distribution functions of fiber length in fiber reinforced thermoplastics 2019transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Amongst the present prediction models of mechanical properties, the Weibull distribution has been introduced to describe the fiber length distribution. However, the Weibull distribution cannot capture the long tail decay, leading to underestimation of the fiber length factor (χ 2). For the first time, two novel modified distribution functions are proposed based on Erlang-2 distribution and Weibull distribution, respectively. The modified Erlang distribution is derived from introducing a shape parameter to capture the sharp peak better, whereas the modified Weibull distribution is developed by introducing a polynomial function instead of the exponential function to reduce the decay rate for the long fibers. The modified distribution functions are investigated by experimental data reported in literatures and the experimental data of GFRPA66 we obtained. The relationship between the shape parameters (α and β) and k can be described by a linear growth function when α >β, and the slope of α~k is larger than that of β~k. The scale parameters (λ, λ α and λ β ) can be considered as the linear growth function of l n. The relationship between the improvement in fiber length factor (Δ) and the improvement in number-average fiber length (δ) can be described by a fitting power function with an offset. In comparison to the Weibull distribution, the modified distribution functions improve more than 4% in χ 2. The modified Weibull distribution tends to capture the actual fiber length distribution for LFT, whereas the modified Erlang distribution captures that for SFT. Amongst the present prediction models of mechanical properties, the Weibull distribution has been introduced to describe the fiber length distribution. However, the Weibull distribution cannot capture the long tail decay, leading to underestimation of the fiber length factor (χ 2). For the first time, two novel modified distribution functions are proposed based on Erlang-2 distribution and Weibull distribution, respectively. The modified Erlang distribution is derived from introducing a shape parameter to capture the sharp peak better, whereas the modified Weibull distribution is developed by introducing a polynomial function instead of the exponential function to reduce the decay rate for the long fibers. The modified distribution functions are investigated by experimental data reported in literatures and the experimental data of GFRPA66 we obtained. The relationship between the shape parameters (α and β) and k can be described by a linear growth function when α >β, and the slope of α~k is larger than that of β~k. The scale parameters (λ, λ α and λ β ) can be considered as the linear growth function of l n. The relationship between the improvement in fiber length factor (Δ) and the improvement in number-average fiber length (δ) can be described by a fitting power function with an offset. In comparison to the Weibull distribution, the modified distribution functions improve more than 4% in χ 2. The modified Weibull distribution tends to capture the actual fiber length distribution for LFT, whereas the modified Erlang distribution captures that for SFT. Fiber length factor Elsevier Fiber length distribution Elsevier Weibull distribution Elsevier Shape and scale parameters Elsevier Zhao, Xianqiong oth Enthalten in Elsevier No title available an international journal Amsterdam [u.a.] (DE-627)ELV013958402 nnns volume:182 year:2019 day:29 month:09 pages:0 https://doi.org/10.1016/j.compscitech.2019.107749 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U GBV_ILN_40 AR 182 2019 29 0929 0 |
allfieldsGer |
10.1016/j.compscitech.2019.107749 doi GBV00000000000738.pica (DE-627)ELV047796693 (ELSEVIER)S0266-3538(19)30622-0 DE-627 ger DE-627 rakwb eng Huang, Dayong verfasserin aut Novel modified distribution functions of fiber length in fiber reinforced thermoplastics 2019transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Amongst the present prediction models of mechanical properties, the Weibull distribution has been introduced to describe the fiber length distribution. However, the Weibull distribution cannot capture the long tail decay, leading to underestimation of the fiber length factor (χ 2). For the first time, two novel modified distribution functions are proposed based on Erlang-2 distribution and Weibull distribution, respectively. The modified Erlang distribution is derived from introducing a shape parameter to capture the sharp peak better, whereas the modified Weibull distribution is developed by introducing a polynomial function instead of the exponential function to reduce the decay rate for the long fibers. The modified distribution functions are investigated by experimental data reported in literatures and the experimental data of GFRPA66 we obtained. The relationship between the shape parameters (α and β) and k can be described by a linear growth function when α >β, and the slope of α~k is larger than that of β~k. The scale parameters (λ, λ α and λ β ) can be considered as the linear growth function of l n. The relationship between the improvement in fiber length factor (Δ) and the improvement in number-average fiber length (δ) can be described by a fitting power function with an offset. In comparison to the Weibull distribution, the modified distribution functions improve more than 4% in χ 2. The modified Weibull distribution tends to capture the actual fiber length distribution for LFT, whereas the modified Erlang distribution captures that for SFT. Amongst the present prediction models of mechanical properties, the Weibull distribution has been introduced to describe the fiber length distribution. However, the Weibull distribution cannot capture the long tail decay, leading to underestimation of the fiber length factor (χ 2). For the first time, two novel modified distribution functions are proposed based on Erlang-2 distribution and Weibull distribution, respectively. The modified Erlang distribution is derived from introducing a shape parameter to capture the sharp peak better, whereas the modified Weibull distribution is developed by introducing a polynomial function instead of the exponential function to reduce the decay rate for the long fibers. The modified distribution functions are investigated by experimental data reported in literatures and the experimental data of GFRPA66 we obtained. The relationship between the shape parameters (α and β) and k can be described by a linear growth function when α >β, and the slope of α~k is larger than that of β~k. The scale parameters (λ, λ α and λ β ) can be considered as the linear growth function of l n. The relationship between the improvement in fiber length factor (Δ) and the improvement in number-average fiber length (δ) can be described by a fitting power function with an offset. In comparison to the Weibull distribution, the modified distribution functions improve more than 4% in χ 2. The modified Weibull distribution tends to capture the actual fiber length distribution for LFT, whereas the modified Erlang distribution captures that for SFT. Fiber length factor Elsevier Fiber length distribution Elsevier Weibull distribution Elsevier Shape and scale parameters Elsevier Zhao, Xianqiong oth Enthalten in Elsevier No title available an international journal Amsterdam [u.a.] (DE-627)ELV013958402 nnns volume:182 year:2019 day:29 month:09 pages:0 https://doi.org/10.1016/j.compscitech.2019.107749 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U GBV_ILN_40 AR 182 2019 29 0929 0 |
allfieldsSound |
10.1016/j.compscitech.2019.107749 doi GBV00000000000738.pica (DE-627)ELV047796693 (ELSEVIER)S0266-3538(19)30622-0 DE-627 ger DE-627 rakwb eng Huang, Dayong verfasserin aut Novel modified distribution functions of fiber length in fiber reinforced thermoplastics 2019transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Amongst the present prediction models of mechanical properties, the Weibull distribution has been introduced to describe the fiber length distribution. However, the Weibull distribution cannot capture the long tail decay, leading to underestimation of the fiber length factor (χ 2). For the first time, two novel modified distribution functions are proposed based on Erlang-2 distribution and Weibull distribution, respectively. The modified Erlang distribution is derived from introducing a shape parameter to capture the sharp peak better, whereas the modified Weibull distribution is developed by introducing a polynomial function instead of the exponential function to reduce the decay rate for the long fibers. The modified distribution functions are investigated by experimental data reported in literatures and the experimental data of GFRPA66 we obtained. The relationship between the shape parameters (α and β) and k can be described by a linear growth function when α >β, and the slope of α~k is larger than that of β~k. The scale parameters (λ, λ α and λ β ) can be considered as the linear growth function of l n. The relationship between the improvement in fiber length factor (Δ) and the improvement in number-average fiber length (δ) can be described by a fitting power function with an offset. In comparison to the Weibull distribution, the modified distribution functions improve more than 4% in χ 2. The modified Weibull distribution tends to capture the actual fiber length distribution for LFT, whereas the modified Erlang distribution captures that for SFT. Amongst the present prediction models of mechanical properties, the Weibull distribution has been introduced to describe the fiber length distribution. However, the Weibull distribution cannot capture the long tail decay, leading to underestimation of the fiber length factor (χ 2). For the first time, two novel modified distribution functions are proposed based on Erlang-2 distribution and Weibull distribution, respectively. The modified Erlang distribution is derived from introducing a shape parameter to capture the sharp peak better, whereas the modified Weibull distribution is developed by introducing a polynomial function instead of the exponential function to reduce the decay rate for the long fibers. The modified distribution functions are investigated by experimental data reported in literatures and the experimental data of GFRPA66 we obtained. The relationship between the shape parameters (α and β) and k can be described by a linear growth function when α >β, and the slope of α~k is larger than that of β~k. The scale parameters (λ, λ α and λ β ) can be considered as the linear growth function of l n. The relationship between the improvement in fiber length factor (Δ) and the improvement in number-average fiber length (δ) can be described by a fitting power function with an offset. In comparison to the Weibull distribution, the modified distribution functions improve more than 4% in χ 2. The modified Weibull distribution tends to capture the actual fiber length distribution for LFT, whereas the modified Erlang distribution captures that for SFT. Fiber length factor Elsevier Fiber length distribution Elsevier Weibull distribution Elsevier Shape and scale parameters Elsevier Zhao, Xianqiong oth Enthalten in Elsevier No title available an international journal Amsterdam [u.a.] (DE-627)ELV013958402 nnns volume:182 year:2019 day:29 month:09 pages:0 https://doi.org/10.1016/j.compscitech.2019.107749 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U GBV_ILN_40 AR 182 2019 29 0929 0 |
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Fiber length factor Fiber length distribution Weibull distribution Shape and scale parameters |
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Huang, Dayong @@aut@@ Zhao, Xianqiong @@oth@@ |
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However, the Weibull distribution cannot capture the long tail decay, leading to underestimation of the fiber length factor (χ 2). For the first time, two novel modified distribution functions are proposed based on Erlang-2 distribution and Weibull distribution, respectively. The modified Erlang distribution is derived from introducing a shape parameter to capture the sharp peak better, whereas the modified Weibull distribution is developed by introducing a polynomial function instead of the exponential function to reduce the decay rate for the long fibers. The modified distribution functions are investigated by experimental data reported in literatures and the experimental data of GFRPA66 we obtained. The relationship between the shape parameters (α and β) and k can be described by a linear growth function when α >β, and the slope of α~k is larger than that of β~k. The scale parameters (λ, λ α and λ β ) can be considered as the linear growth function of l n. The relationship between the improvement in fiber length factor (Δ) and the improvement in number-average fiber length (δ) can be described by a fitting power function with an offset. In comparison to the Weibull distribution, the modified distribution functions improve more than 4% in χ 2. The modified Weibull distribution tends to capture the actual fiber length distribution for LFT, whereas the modified Erlang distribution captures that for SFT.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Amongst the present prediction models of mechanical properties, the Weibull distribution has been introduced to describe the fiber length distribution. However, the Weibull distribution cannot capture the long tail decay, leading to underestimation of the fiber length factor (χ 2). For the first time, two novel modified distribution functions are proposed based on Erlang-2 distribution and Weibull distribution, respectively. The modified Erlang distribution is derived from introducing a shape parameter to capture the sharp peak better, whereas the modified Weibull distribution is developed by introducing a polynomial function instead of the exponential function to reduce the decay rate for the long fibers. The modified distribution functions are investigated by experimental data reported in literatures and the experimental data of GFRPA66 we obtained. The relationship between the shape parameters (α and β) and k can be described by a linear growth function when α >β, and the slope of α~k is larger than that of β~k. The scale parameters (λ, λ α and λ β ) can be considered as the linear growth function of l n. The relationship between the improvement in fiber length factor (Δ) and the improvement in number-average fiber length (δ) can be described by a fitting power function with an offset. In comparison to the Weibull distribution, the modified distribution functions improve more than 4% in χ 2. 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novel modified distribution functions of fiber length in fiber reinforced thermoplastics |
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Novel modified distribution functions of fiber length in fiber reinforced thermoplastics |
abstract |
Amongst the present prediction models of mechanical properties, the Weibull distribution has been introduced to describe the fiber length distribution. However, the Weibull distribution cannot capture the long tail decay, leading to underestimation of the fiber length factor (χ 2). For the first time, two novel modified distribution functions are proposed based on Erlang-2 distribution and Weibull distribution, respectively. The modified Erlang distribution is derived from introducing a shape parameter to capture the sharp peak better, whereas the modified Weibull distribution is developed by introducing a polynomial function instead of the exponential function to reduce the decay rate for the long fibers. The modified distribution functions are investigated by experimental data reported in literatures and the experimental data of GFRPA66 we obtained. The relationship between the shape parameters (α and β) and k can be described by a linear growth function when α >β, and the slope of α~k is larger than that of β~k. The scale parameters (λ, λ α and λ β ) can be considered as the linear growth function of l n. The relationship between the improvement in fiber length factor (Δ) and the improvement in number-average fiber length (δ) can be described by a fitting power function with an offset. In comparison to the Weibull distribution, the modified distribution functions improve more than 4% in χ 2. The modified Weibull distribution tends to capture the actual fiber length distribution for LFT, whereas the modified Erlang distribution captures that for SFT. |
abstractGer |
Amongst the present prediction models of mechanical properties, the Weibull distribution has been introduced to describe the fiber length distribution. However, the Weibull distribution cannot capture the long tail decay, leading to underestimation of the fiber length factor (χ 2). For the first time, two novel modified distribution functions are proposed based on Erlang-2 distribution and Weibull distribution, respectively. The modified Erlang distribution is derived from introducing a shape parameter to capture the sharp peak better, whereas the modified Weibull distribution is developed by introducing a polynomial function instead of the exponential function to reduce the decay rate for the long fibers. The modified distribution functions are investigated by experimental data reported in literatures and the experimental data of GFRPA66 we obtained. The relationship between the shape parameters (α and β) and k can be described by a linear growth function when α >β, and the slope of α~k is larger than that of β~k. The scale parameters (λ, λ α and λ β ) can be considered as the linear growth function of l n. The relationship between the improvement in fiber length factor (Δ) and the improvement in number-average fiber length (δ) can be described by a fitting power function with an offset. In comparison to the Weibull distribution, the modified distribution functions improve more than 4% in χ 2. The modified Weibull distribution tends to capture the actual fiber length distribution for LFT, whereas the modified Erlang distribution captures that for SFT. |
abstract_unstemmed |
Amongst the present prediction models of mechanical properties, the Weibull distribution has been introduced to describe the fiber length distribution. However, the Weibull distribution cannot capture the long tail decay, leading to underestimation of the fiber length factor (χ 2). For the first time, two novel modified distribution functions are proposed based on Erlang-2 distribution and Weibull distribution, respectively. The modified Erlang distribution is derived from introducing a shape parameter to capture the sharp peak better, whereas the modified Weibull distribution is developed by introducing a polynomial function instead of the exponential function to reduce the decay rate for the long fibers. The modified distribution functions are investigated by experimental data reported in literatures and the experimental data of GFRPA66 we obtained. The relationship between the shape parameters (α and β) and k can be described by a linear growth function when α >β, and the slope of α~k is larger than that of β~k. The scale parameters (λ, λ α and λ β ) can be considered as the linear growth function of l n. The relationship between the improvement in fiber length factor (Δ) and the improvement in number-average fiber length (δ) can be described by a fitting power function with an offset. In comparison to the Weibull distribution, the modified distribution functions improve more than 4% in χ 2. The modified Weibull distribution tends to capture the actual fiber length distribution for LFT, whereas the modified Erlang distribution captures that for SFT. |
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title_short |
Novel modified distribution functions of fiber length in fiber reinforced thermoplastics |
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