Larissa Little 2020-07-21
Purpose: When designing structures such as bridges, boats, and planes, the design team needs data about material properties. Often when we engineers first learn about material properties through coursework, we talk about abstract ideas and look up values in tables without ever looking at the data that gave rise to published properties. In this challenge you’ll study an aluminum alloy dataset: Studying these data will give you a better sense of the challenges underlying published material values.
In this challenge, you will load a real dataset, wrangle it into tidy form, and perform EDA to learn more about the data.
Unlike exercises, challenges will be graded. The following rubrics define how you will be graded, both on an individual and team basis.
| Category | Unsatisfactory | Satisfactory |
|---|---|---|
| Effort | Some task q’s left unattempted | All task q’s attempted |
| Observed | Did not document observations | Documented observations based on analysis |
| Supported | Some observations not supported by analysis | All observations supported by analysis (table, graph, etc.) |
| Code Styled | Violations of the style guide hinder readability | Code sufficiently close to the style guide |
| Category | Unsatisfactory | Satisfactory |
|---|---|---|
| Documented | No team contributions to Wiki | Team contributed to Wiki |
| Referenced | No team references in Wiki | At least one reference in Wiki to member report(s) |
| Relevant | References unrelated to assertion, or difficult to find related analysis based on reference text | Reference text clearly points to relevant analysis |
All the deliverables stated in the rubrics above are due on the day of the class discussion of that exercise. See the Syllabus for more information.
library(tidyverse)## ── Attaching packages ─────────────────────────────────────── tidyverse 1.3.0 ──
## ✓ ggplot2 3.3.2 ✓ purrr 0.3.4
## ✓ tibble 3.0.1 ✓ dplyr 1.0.0
## ✓ tidyr 1.1.0 ✓ stringr 1.4.0
## ✓ readr 1.3.1 ✓ forcats 0.5.0
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## x dplyr::filter() masks stats::filter()
## x dplyr::lag() masks stats::lag()
Background: In 1946, scientists at the Bureau of Standards tested a number of Aluminum plates to determine their elasticity and Poisson’s ratio. These are key quantities used in the design of structural members, such as aircraft skin under buckling loads. These scientists tested plats of various thicknesses, and at different angles with respect to the rolling direction.
The readr package in the Tidyverse contains functions to load data
form many sources. The read_csv() function will help us load the data
for this challenge.
## NOTE: If you extracted all challenges to the same location,
## you shouldn't have to change this filename
filename <- "./data/stang.csv"
## Load the data
df_stang <- read_csv(filename)## Parsed with column specification:
## cols(
## thick = col_double(),
## E_00 = col_double(),
## mu_00 = col_double(),
## E_45 = col_double(),
## mu_45 = col_double(),
## E_90 = col_double(),
## mu_90 = col_double(),
## alloy = col_character()
## )
df_stang## # A tibble: 9 x 8
## thick E_00 mu_00 E_45 mu_45 E_90 mu_90 alloy
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <chr>
## 1 0.022 10600 0.321 10700 0.329 10500 0.31 al_24st
## 2 0.022 10600 0.323 10500 0.331 10700 0.323 al_24st
## 3 0.032 10400 0.329 10400 0.318 10300 0.322 al_24st
## 4 0.032 10300 0.319 10500 0.326 10400 0.33 al_24st
## 5 0.064 10500 0.323 10400 0.331 10400 0.327 al_24st
## 6 0.064 10700 0.328 10500 0.328 10500 0.32 al_24st
## 7 0.081 10000 0.315 10000 0.32 9900 0.314 al_24st
## 8 0.081 10100 0.312 9900 0.312 10000 0.316 al_24st
## 9 0.081 10000 0.311 -1 -1 9900 0.314 al_24st
Note that these data are not tidy! The data in this form are convenient for reporting in a table, but are not ideal for analysis.
q1 Tidy df_stang to produce df_stang_long. You should have
column names thick, alloy, angle, E, mu. Make sure the angle
variable is of correct type. Filter out any invalid values.
Hint: You can reshape in one pivot using the ".value" special
value for names_to.
## TASK: Tidy `df_stang`
df_stang_long <-
df_stang %>%
pivot_longer(c(-thick, -alloy),
names_to = c(".value", 'angle'),
names_sep = '_',
values_drop_na = TRUE) %>%
filter(E>0)
df_stang_long$angle = as.integer(df_stang_long$angle)
df_stang_long## # A tibble: 26 x 5
## thick alloy angle E mu
## <dbl> <chr> <int> <dbl> <dbl>
## 1 0.022 al_24st 0 10600 0.321
## 2 0.022 al_24st 45 10700 0.329
## 3 0.022 al_24st 90 10500 0.31
## 4 0.022 al_24st 0 10600 0.323
## 5 0.022 al_24st 45 10500 0.331
## 6 0.022 al_24st 90 10700 0.323
## 7 0.032 al_24st 0 10400 0.329
## 8 0.032 al_24st 45 10400 0.318
## 9 0.032 al_24st 90 10300 0.322
## 10 0.032 al_24st 0 10300 0.319
## # … with 16 more rows
Use the following tests to check your work.
## NOTE: No need to change this
## Names
assertthat::assert_that(
setequal(
df_stang_long %>% names,
c("thick", "alloy", "angle", "E", "mu")
)
)## [1] TRUE
## Dimensions
assertthat::assert_that(all(dim(df_stang_long) == c(26, 5)))## [1] TRUE
## Type
assertthat::assert_that(
(df_stang_long %>% pull(angle) %>% typeof()) == "integer"
)## [1] TRUE
print("Very good!")## [1] "Very good!"
q2 Perform a basic EDA on the aluminum data without visualization. Use your analysis to answer the questions under observations below. In addition, add your own question that you’d like to answer about the data.
df_stang_long %>%
group_by(alloy) %>%
summarize(avg_E = mean(E),
max_E = max(E),
min_E = min(E),
sd_E_pct = sd(E)/mean(E)*100,
avg_mu = mean(mu),
max_mu = max(mu),
min_mu = min(mu),
sd_mu_pct = sd(mu)/mean(mu)*100
)## `summarise()` ungrouping output (override with `.groups` argument)
## # A tibble: 1 x 9
## alloy avg_E max_E min_E sd_E_pct avg_mu max_mu min_mu sd_mu_pct
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 al_24st 10335. 10700 9900 2.60 0.321 0.331 0.31 2.10
df_stang_long %>%
group_by(alloy, angle) %>%
summarize(avg_E = mean(E),
max_E = max(E),
min_E = min(E),
sd_E_pct = sd(E)/mean(E)*100,
avg_mu = mean(mu),
max_mu = max(mu),
min_mu = min(mu),
sd_mu_pct = sd(mu)/mean(mu)*100
)## `summarise()` regrouping output by 'alloy' (override with `.groups` argument)
## # A tibble: 3 x 10
## # Groups: alloy [1]
## alloy angle avg_E max_E min_E sd_E_pct avg_mu max_mu min_mu sd_mu_pct
## <chr> <int> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 al_24st 0 10356. 10700 10000 2.61 0.320 0.329 0.311 2.02
## 2 al_24st 45 10362. 10700 9900 2.63 0.324 0.331 0.312 2.14
## 3 al_24st 90 10289. 10700 9900 2.81 0.320 0.33 0.31 2.06
df_stang_long %>%
group_by(alloy, thick) %>%
summarize(avg_E = mean(E),
max_E = max(E),
min_E = min(E),
sd_E_pct = sd(E)/mean(E)*100,
avg_mu = mean(mu),
max_mu = max(mu),
min_mu = min(mu),
sd_mu_pct = sd(mu)/mean(mu)*100
)## `summarise()` regrouping output by 'alloy' (override with `.groups` argument)
## # A tibble: 4 x 10
## # Groups: alloy [1]
## alloy thick avg_E max_E min_E sd_E_pct avg_mu max_mu min_mu sd_mu_pct
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 al_24st 0.022 10600 10700 10500 0.844 0.323 0.331 0.31 2.29
## 2 al_24st 0.032 10383. 10500 10300 0.725 0.324 0.33 0.318 1.57
## 3 al_24st 0.064 10500 10700 10400 1.04 0.326 0.331 0.32 1.22
## 4 al_24st 0.081 9975 10100 9900 0.709 0.314 0.32 0.311 0.912
Observations:
-
Is there “one true value” for the material properties of Aluminum? No there is a spread between 9900-10700 (1000 lbs/in^2) for E and of 0.310-0.331 for mu.
-
How many aluminum alloys were tested? How do you know? Only one alloy was tested, can tell by grouping by that alloy
-
What angles were tested? Angles tested were 0, 45, and 90
-
What thicknesses were tested? Thicknesses of 0.022, 0.032, 0.064, and 0.081 (inches)
-
Did the E and mu vary for the different angles?
q3 Create a visualization to investigate your question from q1 above. Can you find an answer to your question using the dataset? Would you need additional information to answer your question?
df_stang_long %>%
ggplot(aes(mu, fill = angle)) +
geom_histogram(binwidth = 0.01) +
facet_wrap(vars(angle)) +
ggtitle("Distribution of poisson ratio by angle")
Observations
It looks like mu may have some angle dependence, but it is hard to tell with the small number of observations we have here.
df_stang_long$angle = as.character(df_stang_long$angle)
df_stang_long %>%
ggplot(aes(E,angle, color = angle)) +
geom_boxplot() +
coord_flip() +
ggtitle("Distribution of tensile modulus by angle")
df_stang_long %>%
ggplot(aes(E, fill = angle)) +
geom_histogram(binwidth = 250) +
facet_wrap(vars(angle)) +
ggtitle("Distribution of tensile modulus by angle")
df_stang_long %>%
ggplot(aes(E, color = angle)) +
geom_density() +
ggtitle("Distribution of tensile modulus by angle")
Observations:
- E does not seem to have an angle dependence. It is worth noting that the number of data point is small. Each ‘quartile’ in the box plot is only comprised of 2 data points, so using the box plot visualization may be misleading.
If we consider the histogram visualization, it seems that there may be a difference in the poissons ration of the 45 angle samples, but the difference in the tensile modulus values looks minimal.
q4 Consider the following statement:
“A material’s property (or material property) is an intensive property of some material, i.e. a physical property that does not depend on the amount of the material.”[2]
Note that the “amount of material” would vary with the thickness of a
tested plate. Does the following graph support or contradict the claim
that “elasticity E is an intensive material property.” Why or why not?
Is this evidence conclusive one way or another? Why or why not?
## NOTE: No need to change; run this chunk
df_stang_long %>%
ggplot(aes(mu, E, color = as_factor(thick))) +
geom_point(size = 3) +
theme_minimal()
Observations:
- It seems that the samples with a thickness of 0.081 had different properties than the other thicknesses, which do not seem to be distinct from one another.
So it seems that either something was different about those samples, or there is some thickness cut-off below which the E and mu do not change as a function of thickness.
There are not very many observations at each thickness, so I would not call this observation ‘conclusive’
[1] Stang, Greenspan, and Newman, “Poisson’s ratio of some structural alloys for large strains” (1946) Journal of Research of the National Bureau of Standards, (pdf link)[https://nvlpubs.nist.gov/nistpubs/jres/37/jresv37n4p211_A1b.pdf]
[2] Wikipedia, List of material properties, accessed 2020-06-26, (link)[https://en.wikipedia.org/wiki/List_of_materials_properties]