This function takes a vector of strength values and a vector of measured thicknesses, and a nominal thickness and returns the normalized strength.
normalize_ply_thickness(strength, measured_thk, nom_thk)the strength to be normalized. Either a vector or a numeric
the measured thickness of the samples. Must be the same length as strength
the nominal thickness. Must be a single numeric value.
The normalized strength values
It is often necessary to normalize strength values so that variation in specimen thickness does not unnecessarily increase variation in strength. See CMH-17-1G, or other references, for information about the cases where normalization is appropriate.
Either cured ply thickness or laminate thickness may be used for
measured_thk and nom_thk, as long as the same decision
made for both values.
The formula applied is: $$normalized\,value = test\,value \frac{t_{measured}}{t_{nominal}}$$
If you need to normalize based on fiber volume fraction (or another method), you will first need to calculate the nominal cured ply thickness (or laminate thickness). Those calculations are outside the scope of this documentation.
“Composite Materials Handbook, Volume 1. Polymer Matrix Composites Guideline for Characterization of Structural Materials,” SAE International, CMH-17-1G, Mar. 2012.
library(dplyr)
carbon.fabric.2 %>%
select(thickness, strength) %>%
mutate(normalized_strength = normalize_ply_thickness(strength,
thickness,
0.105)) %>%
head(10)
#> thickness strength normalized_strength
#> 1 0.112 142.817 152.3381
#> 2 0.113 135.901 146.2554
#> 3 0.113 132.511 142.6071
#> 4 0.112 135.586 144.6251
#> 5 0.113 125.145 134.6799
#> 6 0.113 135.203 145.5042
#> 7 0.113 128.547 138.3411
#> 8 0.113 127.709 137.4392
#> 9 0.113 127.074 136.7558
#> 10 0.114 126.879 137.7543
## thickness strength normalized_strength
## 1 0.112 142.817 152.3381
## 2 0.113 135.901 146.2554
## 3 0.113 132.511 142.6071
## 4 0.112 135.586 144.6251
## 5 0.113 125.145 134.6799
## 6 0.113 135.203 145.5042
## 7 0.113 128.547 138.3411
## 8 0.113 127.709 137.4392
## 9 0.113 127.074 136.7558
## 10 0.114 126.879 137.7543