Investigating the relationship between carburising time and case depth in steel case hardened by pack carburising, gas carbontriding and cyaniding techniques

A Scientific Research Project produced for the HSC Science Extension course, 2020

ABSTRACT Confirmation into the significance of the relationship between carburising time and case depth in steel is lacking in modern research. The following investigation tests the significance of the relationship between carburising time and case depth in steel for pack carburising, gas carbonitriding and cyaniding case hardening techniques. The significance of the difference in case depth produced by each case hardening technique for typical carburising times is established. Through first-hand experimentation, primary quantitative data was collected by carburising steel samples for 1hr, 2hr, 3hr, 4hr and 5hr by each case hardening technique. Case depth was measured for each sample metallographically. Statistical testing and data modelling revealed a significant relationship between carburising time and case depth for each case hardening technique. Analysis also revealed significance in the difference in case depth across each case hardening technique investigated. Findings of the investigation were used to refute null hypotheses, concluding the relationship between carburising time and case depth as significant. It was also concluded that the difference in case depth produced by pack carburising, gas carbonitriding and cyaniding is significant, whereby maximum achieved case depth for each technique is in order of greatest to least: pack carburising, gas carbonitriding, cyaniding.

LITERATURE REVIEW The ability to modify specific properties of materials controllably holds significance in modern society.^{1, 2} Thus, development of heat treatment techniques to modify service properties of steel has become essential in modern engineering, as steel maintains extensive use globally.^{3, 4} Increasing demands for reliable steel components in a range of industries requires extensive knowledge for producing wear-resistant and tough steel components through heat treatment to avoid potentially catastrophic failure of critical components.^{5} Common heat treatment processes used to enhance wear-resistance and toughness of steels include case hardening.^{6, 7} Case hardening achieves improvement of properties through modification of the steel microstructure,^{7, 8} specifically the arrangement of microstructural phases (homogenous states of matter in the form of grains with unique chemical compositions).^{8, 9} The carbon-soluble austenite phase and hard martensite phase are essential in case hardening practice.^{8, 9} See Appendix 1 for phase data.

Generally, case hardening involves creating a hardened layer (case) on the surface of a steel component, with the core remaining relatively soft.^{6, 7} Case hardening techniques commonly rely on the mechanism of carburisation (also known as carburising), followed by quenching.^{6, 7 } Carburisation is a process whereby austenitic steel is brought into contact with a carbon-rich environment (carbon potential) at elevated temperatures.^{6, 7, 9} The difference in carbon concentration between the steel and the carburising environment results in carbon absorbing into surficial austenite via diffusion to produce a carbon-rich case at the steel surface.^{6, 7, 9, 10} Initial surface diffusion establishes a carbon concentration gradient in the steel, encouraging further carbon diffusion towards the core.^{6, 10} To achieve a hardened case, carburised steels are cooled rapidly via quenching in water or oil.^{6, 7, 8} Rapid cooling prevents dissolved carbon to diffuse out of austenite grains, forming a hard martensitic case.^{6, 7, 8, 9 } Cases may also be formed by simultaneous absorption of carbon and nitrogen into austenitic steel via diffusion.^{6, 7, 10} This mechanism is known as carbonitriding.^{6, 7 }Absorption of nitrogen into the steel microstructure disrupts the crystalline structure of each grain, reducing carbon diffusion efficiency and resulting in shallower case depths compared to carburised steels.^{6, 7, 10} Absorbed nitrogen may additionally lead to formation of nitrides upon quenching, further increasing surface hardness.^{6, 7, 12} In accordance to diffusion theory, total case depth depends on time given for carburising, hardening element (carbon/nitrogen) concentrations in the carburising environment, and carburising temperature.^{6, 7} Combined properties of the hardened case superimposed on a relatively soft core produce a wear-resistant and tough component.^{6, 7, 8 }

A range of specialised case hardening techniques are used in industry.^{7}Pack Carburising relies on carburising steel components in the presence of solid carbonaceous material packed around the component.^{6, 7, 11}Gas Carbonitriding involves carbonitriding components in the presence of dissociated carbon monoxide (CO) and ammonia (NH_{4}) gas.^{6, 7, 11 }Cyaniding requires steel components to be carbonitrided in a specialised metal-cyanide bath.^{6, 7, 11} Cases produced by cyaniding are generally shallower than those produced by gas carbonitriding due to higher concentrations of nitrogen in the carbonitriding environment, resulting in greater nitrogen diffusion and reduced carbon diffusion efficiency.^{6, 8, 11}

Physical properties of case hardened components depend on case depth and case phase composition,^{6, 7, 11, 13} enabling manipulation of case hardened steel properties by producing different case depths.^{6, 7} It is common to produce different total case depths by changing the carburising time given.^{7, 13} When carburising conditions are consistent, total case depth is given by:

d = ϕ√t

where d is total case depth, t is carburising time and ϕis a temperature-dependent constant.^{6, 7, 13} This relationship is expected for all case hardening techniques where temperature and hardening element concentrations are maintained.^{6} If these variables are not controlled, case depth is not expected to fit this model. In pack carburising, carbon potential decreases as carburisation progresses.^{6,7} Therefore, empirical relationships between carburising time and case depth are expected to deviate from this model for pack carburising. For gas carbonitriding and cyaniding, hardening element concentrations are maintained more effectively.^{6, 7} Hence, it is predicted that the relationship between variables will fit this model more strongly for gas carbonitriding and cyaniding.

Numerous studies have investigated physical properties of case hardened steels, however research into the relationship between carburising time and case depth for different case hardening methods is lacking. Mesmari, H et al. (2010) investigated optimal carburising temperatures and carburising times for pack carburised steel, concluding that carburising steel for 4 hours at 950°C produced most adequate results for high-performance gears. Their research acknowledged and discussed trends between carburising time and case depth for their results. Mesmari, H et al. are commended for investigating a broad range of carburising times and temperatures, however their research is limited by the absence of statistical testing to determine and evaluate significance of the relationship between carburising time/temperature and case depth. Adetunji, O et al. (2015) investigated tensile strength and hardness of case hardened steel compared to quench-hardened (not carburised) steel. Their research was significantly limited by ignoring the influence of case depth on mechanical properties. Similarly, Björkeborn, K et al. (2009) ignored the influence of case depth on case hardened steel properties in their investigation into the machinability of case hardened steel. Both Adetunji, O et al. and Björkeborn, K et al. failed to acknowledge the carburising time, temperature and case hardening technique for the steel tested in their respective investigations, indicating a deficiency in case hardening knowledge.

The lack of confirmatory research into statistically testing a relationship between carburising time and total case depth is indicative in modern research. Despite active use in industry, the relationship between case depth and carburising time has not recently been statistically tested for gas carbonitriding and cyaniding. According to Panizzi, L (2010), understanding relationships between carburising time and case depth is necessary as the properties of case hardened components are dependent on case depth.^{14} Further research into this field will be useful in quantitatively confirming a significant relationship between carburising time and case depth for various case hardening techniques.

RESEARCH QUESTION How does carburising time affect total case depth in steel case hardened by pack carburising, gas carbonitriding and cyaniding?

This Research Question was approached in two sections: 1. Is the relationship between carburising time and total case depth significant? 2. Is the difference in total case depth between each case hardening technique significant for typical carburising times?

HYPOTHESIS Hypothesis 1: The relationship between carburising time and case depth is significant, whereby increasing the carburising time period subsequently increases total case depth. Null Hypothesis 1 states there is no relationship between carburising time and total case depth.

Hypothesis 2: The difference in total case depth between case hardening techniques is significant for typical carburising times. The maximum achieved case depth for each technique will be in order of greatest to least: pack carburising, gas carbonitriding, cyaniding. Null Hypothesis 2 states there is no significance in the difference in total case depth between case hardening techniques.

METHODOLOGY Data Collection Through first-hand experimentation, the methodology yielded primary quantitative data for case depth of case-hardened steel, enabling opportunity for quantitative analysis.^{15} Five 1020 BMS rod samples ^{12} were designated to each case hardening technique (pack carburising, gas carbonitriding and cyaniding). Samples were cut to identical sizes at low temperatures to prevent inconsistent microstructural changes, ensuring validity.^{12} One sample from each group of five was designated typical carburising times of 1hr, 2hr, 3hr, 4hr and 5hr respectively.^{11} Samples were appropriately case hardened by a heat treatment specialist.^{11 }Reliability, accuracy and validity were augmented through strict control of carburising conditions by the heat treatment specialist.^{11 }Treated samples were prepared by a metallurgist for metallographic examination.^{12, 16, 6} 40 measurements of case depth were taken for each sample on a metallurgical microscope using an eyepiece graticule at 50X magnification.^{12} Validity and accuracy were ensured by calibrating the microscope prior to use.^{12}

Data Analysis Data was cleansed using methods outlined by Sharma, R (2020). Experimental uncertainty was estimated by determining the greatest difference between the mean and individual measurements for each sample (Max(x_{1} – _{mean}))^{17}. Scatter graphs and linear models were produced for mean data from each case hardening technique, enabling comparison between two numeric variables.^{18} Mean case depth values were additionally graphed against the square root of carburising time, linearising the expected model.^{19} The R-squared (R^{2}) value, correlation coefficient (r) and standard error of the estimate (SEE) were determined for each model.^{20, 21}

To quantitatively test Hypothesis 1, two-tailed independent t-tests were conducted to determine whether the difference in means between case depths for successive carburising times were statistically significant.^{21, 22, 23} This specific t-test was selected as it compares the means of two continuous variables.^{11, 12} A p-value <0.05 was used to accept statistical significance of the difference of means.^{11, 12 }The relationship between case depth and carburising time was deemed to be statistically significant if the difference in means was found to be significant, rejecting Null Hypothesis 1.^{22, 23} To quantitatively test Hypothesis 2, differences in mean case depths were compared across each case hardening technique using two-tailed independent t-tests.^{22, 23} If the majority of the differences in means were significant, the difference in case depth across case hardening techniques was deemed significant, refuting Null Hypothesis 2.^{21, 22, 23}

RESULTS Summary Statistics Table 1 shows mean case depth produced for each designated carburising time and case hardening method, including estimated uncertainty. The greatest estimated uncertainty is ±0.14mm. 1.96 standard deviations (1.96σ) describes the spread of the middle 95% of the data from the mean value. Sample size was identical for each sample.

Sample Histogram

Graphs and Models for Empirical Data Graphs produced for pack carburising and gas carbonitriding appear to coincide with the expected relationship (see Figure 2). Graphsfor cyaniding demonstrate a linear relationship between carburising time and case depth.

Difference in Mean Tables The difference in means between case depth for successive carburising times was found to be statistically significant (see Table 3).

Comparing mean case depth across each case hardening technique demonstrated that majority of the compared means were statistically significant (see Table 4).

DISCUSSION Answering Research Question Section 1 Results demonstrated that case depth increases as carburising time increases. For pack carburising, the linearised model (Figure 2b) indicated strong correlation between carburising time and case depth, whereby r = 0.89.^{24} Strong correlation was observed in the linearised model (Figure 2d) for gas carbonitriding, yielding r = 0.96.^{1} A linear model (Figure 2e) fitted data for cyaniding with the strongest correlation, producing a very strong correlation of r = 0.99.^{24} A statistically significant relationship between carburising time and case depth was found for each case hardening technique through testing Hypothesis 1.^{23} Taking all evidence into account, Null Hypothesis 1 is refuted and statistical significance of the relationship between carburising time and case depth is confirmed. Significance of these relationships imply that case depth can be accurately predicted for select carburising times. The observed relationship between carburising time and case depth coincides with case hardening theory. In accordance to diffusion theory, increasing time given for carburisation/carbonitriding causes an increase in the amount of diffused carbon/nitrogen in the steel, subsequently increasing case depth. ^{6, 7}

Answering Research Question Section 2 Through testing Hypothesis 2, difference in case depth between case hardening techniques was found to be significant for typical carburising times, as the majority of the case depths compared across case hardening methods were significant.^{23} Maximum achieved case depth (carburising time 5hrs) was in order of greatest to least: pack carburising, gas carbonitriding, cyaniding. Comparing graphs across case hardening methods revealed that relationships between variables was unique for each technique. Figure 2a (pack carburising) indicated a definite plateau in case depth between the 3hr, 4hr and 5hr carburising times. A plateau of this degree was not observed qualitatively in gas carbonitriding and cyaniding graphs. Figure 2e (cyaniding) demonstrated a linear relationship between variables unlike the other graphs. Taking all evidence into account, Null Hypothesis 2 is refuted and the significance in the difference in case depth between each of the case hardening techniques is confirmed.

The differences in relationships across case hardening methods corresponds with expectations from theory. In pack carburising, carbon potential is not replenished as carbon diffuses into the steel.^{6, 7} Thus, quantities of carbon available for absorption into the steel decreases, resulting in actual case depth values deviating from the expected d = ϕ√t model.^{6} In gas carbonitriding, hardening element concentrations are maintained more effectively, enabling carbon/nitrogen diffusion consistent with d = ϕ√t ^{6, 7} Despite expectations that the relationship for cyaniding coincides with the model d = ϕ√t due to effectively maintained hardening element concentrations, Figure 2e suggested the relationship was linear. The apparent linear relationship may result from high quantities of absorbed nitrogen in the steel impacting the expected nature for hardening element diffusion, subsequently influencing case depth.

Evaluating Reliability Standard deviations (95% CI) were used to evaluate consistency of measurements. The largest standard deviations (as percentages of the mean) for pack carburising, gas carbonitriding and cyaniding measurements were 2.91%, 15.6% and 10.1% respectively. Despite poorer consistency for gas carbonitriding and cyaniding, reliability is considered sufficient for the investigation as both Research Questions were successfully addressed. Adequate consistency of results identifies that strict measures taken by the heat treatment specialist and metallurgist to reduce random errors in the Methodology were effective.

Evaluating Accuracy Accuracy was estimated by considering uncertainty of measurements and SEE (95% CI) for the mathematical models. The greatest experimental uncertainty (calculated via Max(x_{1} –_{mean})) across all data was 10.6% (±0.14mm). Qualitatively, pack carburising and gas carbonitriding graphs appeared to correspond with the expected relationship. Figure 2b and Figure 2d demonstrated a SEE of ±0.36 and ±0.25 respectively, presenting a small error margin for each model. The SEE for Figure 2e was ±0.052 demonstrating exceptional accuracy. Although Figure 2e appeared linear (unlike the expected model), it is unlikely that systematic errors caused this. Although uncertainty was significant, accuracy is considered to be sufficient for addressing both Research Questions as the SEE for each graph was minor, and most graphs qualitatively fit expectations. As measurements and models demonstrated accuracy, it is decided that the measures taken by the heat treatment specialist and metallurgist were adequate in reducing systematic errors.

Evaluating Validity The results enabled successful testing of Hypothesis 1 and Hypothesis 2 as per the intention of the investigation. Methodologies for data analysis are considered valid, as the analysis process was supported extensively by academic resources. Successful confirmation of reliability and accuracy provided evidence of the sufficient control measures taken by the heat treatment specialist and metallurgist in experimentation and data collection. The investigation is considered to be sufficiently valid.

Limitations & Recommendations for Future Investigation Not being able to confirm similar results for other steel grades limited the investigation. Available time and resources limited the range of carburising times and case hardening techniques explored. The inability to perform statistical tests to compare each model to the expected model limited the extent of data analysis.

It is recommended that further testing is conducted into the relationship between carburising time and case depth for a broader range of steel grades. It is also recommended that models produced for each case hardening technique are statistically tested.

CONCLUSION The investigation successfully addressed both Research Questions and Hypotheses by the collection and analysis of quantitative data through first-hand experimentation.

Through testing Hypothesis 1, a statistically significant relationship between total carburising time and case depth in steel has been determined for pack carburising, gas carbonitriding and cyaniding. Results demonstrated that as carburising time increases, case depth increases. Thus, Null Hypothesis 1 is refuted, and Hypothesis 1 is supported.

Through testing Hypothesis 2, the difference in total case depth between each case hardening technique is determined to be statistically significant for typical carburising times, whereby maximum achieved case depth for each technique (carburising time 5hrs) is in order of greatest to least: pack carburising, gas carbonitriding, cyaniding. Graphs for pack carburising deviated moderately from the expected relationship. Qualitatively, gas carbonitriding graphs corresponded to the expected model, while cyaniding graphs appeared linear. Thus, Null Hypothesis 2 is refuted, and Hypothesis 2 is supported. Through evaluation of results, strict control measures taken by the heat treatment specialist and metallurgist during experimentation were found to be sufficient in reducing random and systematic errors. Data collected was successfully analysed to fulfil the requirements of both Research Questions, indicating validity of the methodology. The results and methodology were deemed to be sufficiently reliable, accurate and valid for this investigation. It is recommended that relationships between carburising time and case depth are investigated for a wider range of case hardening techniques and carburising times.

[2] Dobrzanski, Leszek. 2006, Significance of materials science for the future development of societies. Journal of Materials Processing Technology. 175. 133-148.

[6] American Society of Metals, 1977, Carburizing and Carbonitriding, American Society of Metals, United States of America.

[7] Dossett, J & Totten, G 2013, ‘Introduction to Surface Hardening of Steels*’, ASM International, vol. 4A, pp. 1-10, viewed 1 November 2019, ASM International.

[8] Capudean, B 2003, Metallurgy Matters: Phases, structures, and the influences of temperature, The Fabricator, viewed 23 October 2019.

Conrad PetrovicInvestigating the relationship between carburising time and case depth in steel case hardened by pack carburising, gas carbontriding and cyaniding techniques

A Scientific Research Project produced for the HSC Science Extension course, 2020ABSTRACTConfirmation into the significance of the relationship between carburising time and case depth in steel is lacking in modern research. The following investigation tests the significance of the relationship between carburising time and case depth in steel for pack carburising, gas carbonitriding and cyaniding case hardening techniques. The significance of the difference in case depth produced by each case hardening technique for typical carburising times is established. Through first-hand experimentation, primary quantitative data was collected by carburising steel samples for 1hr, 2hr, 3hr, 4hr and 5hr by each case hardening technique. Case depth was measured for each sample metallographically. Statistical testing and data modelling revealed a significant relationship between carburising time and case depth for each case hardening technique. Analysis also revealed significance in the difference in case depth across each case hardening technique investigated. Findings of the investigation were used to refute null hypotheses, concluding the relationship between carburising time and case depth as significant. It was also concluded that the difference in case depth produced by pack carburising, gas carbonitriding and cyaniding is significant, whereby maximum achieved case depth for each technique is in order of greatest to least: pack carburising, gas carbonitriding, cyaniding.

LITERATURE REVIEWThe ability to modify specific properties of materials controllably holds significance in modern society.

^{1, 2}Thus, development of heat treatment techniques to modify service properties of steel has become essential in modern engineering, as steel maintains extensive use globally.^{3, 4}Increasing demands for reliable steel components in a range of industries requires extensive knowledge for producing wear-resistant and tough steel components through heat treatment to avoid potentially catastrophic failure of critical components.^{5}Common heat treatment processes used to enhance wear-resistance and toughness of steels includecase hardening.^{6, 7}Case hardening achieves improvement of properties through modification of the steelmicrostructure,^{7, 8}specifically the arrangement of microstructuralphases(homogenous states of matter in the form ofgrainswith unique chemical compositions).^{8, 9}The carbon-solubleaustenitephase and hardmartensitephase are essential in case hardening practice.^{8, 9}SeeAppendix 1for phase data.Generally, case hardening involves creating a hardened layer (

case) on the surface of a steel component, with the core remaining relatively soft.^{6, 7}Case hardening techniques commonly rely on the mechanism ofcarburisation(also known ascarburising), followed by quenching.^{6, 7 }Carburisation is a process whereby austenitic steel is brought into contact with a carbon-rich environment (carbon potential) at elevated temperatures.^{6, 7, 9}The difference in carbon concentration between the steel and the carburising environment results in carbon absorbing into surficial austenite via diffusion to produce a carbon-richcaseat the steel surface.^{6, 7, 9, 10}Initial surface diffusion establishes a carbon concentration gradient in the steel, encouraging further carbon diffusion towards the core.^{6, 10}To achieve a hardened case, carburised steels are cooled rapidly via quenching in water or oil.^{6, 7, 8}Rapid cooling prevents dissolved carbon to diffuse out of austenite grains, forming a hard martensitic case.^{6, 7, 8, 9 }Cases may also be formed by simultaneous absorption of carbon and nitrogen into austenitic steel via diffusion.^{6, 7, 10}This mechanism is known ascarbonitriding.^{6, 7 }Absorption of nitrogen into the steel microstructure disrupts the crystalline structure of each grain, reducing carbon diffusion efficiency and resulting in shallower case depths compared to carburised steels.^{6, 7, 10}Absorbed nitrogen may additionally lead to formation of nitrides upon quenching, further increasing surface hardness.^{6, 7, 12}In accordance to diffusion theory,total case depthdepends on time given for carburising,hardening element(carbon/nitrogen) concentrations in the carburising environment, and carburising temperature.^{6, 7}Combined properties of the hardened case superimposed on a relatively soft core produce a wear-resistant and tough component.^{6, 7, 8 }A range of specialised case hardening techniques are used in industry.

^{7}relies on carburising steel components in the presence of solid carbonaceous material packed around the component.Pack Carburising^{6, 7, 11}involves carbonitriding components in the presence of dissociated carbon monoxide (CO) and ammonia (NHGas Carbonitriding_{4}) gas.^{6, 7, 11 }requires steel components to be carbonitrided in a specialised metal-cyanide bath.Cyaniding^{6, 7, 11}Cases produced by cyaniding are generally shallower than those produced by gas carbonitriding due to higher concentrations of nitrogen in the carbonitriding environment, resulting in greater nitrogen diffusion and reduced carbon diffusion efficiency.^{6, 8, 11}Physical properties of case hardened components depend on case depth and case phase composition,

^{6, 7, 11, 13}enabling manipulation of case hardened steel properties by producing different case depths.^{6, 7}It is common to produce different total case depths by changing the carburising time given.^{7, 13}When carburising conditions are consistent, total case depth is given by:d = ϕ√twhere

dis total case depth,tis carburising time andϕis a temperature-dependent constant.^{6, 7, 13}This relationship is expected for all case hardening techniques where temperature and hardening element concentrations are maintained.^{6}If these variables are not controlled, case depth is not expected to fit this model. In pack carburising, carbon potential decreases as carburisation progresses.^{6,7}Therefore, empirical relationships between carburising time and case depth are expected to deviate from this model for pack carburising. For gas carbonitriding and cyaniding, hardening element concentrations are maintained more effectively.^{6, 7}Hence, it is predicted that the relationship between variables will fit this model more strongly for gas carbonitriding and cyaniding.Numerous studies have investigated physical properties of case hardened steels, however research into the relationship between carburising time and case depth for different case hardening methods is lacking. Mesmari, H et al. (2010) investigated optimal carburising temperatures and carburising times for pack carburised steel, concluding that carburising steel for 4 hours at 950°C produced most adequate results for high-performance gears. Their research acknowledged and discussed trends between carburising time and case depth for their results. Mesmari, H et al. are commended for investigating a broad range of carburising times and temperatures, however their research is limited by the absence of statistical testing to determine and evaluate significance of the relationship between carburising time/temperature and case depth. Adetunji, O et al. (2015) investigated tensile strength and hardness of case hardened steel compared to quench-hardened (not carburised) steel. Their research was significantly limited by ignoring the influence of case depth on mechanical properties. Similarly, Björkeborn, K et al. (2009) ignored the influence of case depth on case hardened steel properties in their investigation into the machinability of case hardened steel. Both Adetunji, O et al. and Björkeborn, K et al. failed to acknowledge the carburising time, temperature and case hardening technique for the steel tested in their respective investigations, indicating a deficiency in case hardening knowledge.

The lack of confirmatory research into statistically testing a relationship between carburising time and total case depth is indicative in modern research. Despite active use in industry, the relationship between case depth and carburising time has not recently been statistically tested for gas carbonitriding and cyaniding. According to Panizzi, L (2010), understanding relationships between carburising time and case depth is necessary as the properties of case hardened components are dependent on case depth.

^{14}Further research into this field will be useful in quantitatively confirming a significant relationship between carburising time and case depth for various case hardening techniques.RESEARCH QUESTIONHow does carburising time affect total case depth in steel case hardened by pack carburising, gas carbonitriding and cyaniding?This Research Question was approached in two sections:

1. Is the relationship between carburising time and total case depth significant?

2. Is the difference in total case depth between each case hardening technique significant for typical carburising times?

HYPOTHESISHypothesis 1:

The relationship between carburising time and case depth is significant, whereby increasing the carburising time period subsequently increases total case depth.

Null Hypothesis 1 states there is no relationship between carburising time and total case depth.

Hypothesis 2:

The difference in total case depth between case hardening techniques is significant for typical carburising times. The maximum achieved case depth for each technique will be in order of greatest to least: pack carburising, gas carbonitriding, cyaniding.

Null Hypothesis 2 states there is no significance in the difference in total case depth between case hardening techniques.

METHODOLOGYData CollectionThrough first-hand experimentation, the methodology yielded primary quantitative data for case depth of case-hardened steel, enabling opportunity for quantitative analysis.

^{15}Five 1020 BMS rod samples

^{12}were designated to each case hardening technique (pack carburising, gas carbonitriding and cyaniding). Samples were cut to identical sizes at low temperatures to prevent inconsistent microstructural changes, ensuring validity.^{12}One sample from each group of five was designated typical carburising times of 1hr, 2hr, 3hr, 4hr and 5hr respectively.^{11}Samples were appropriately case hardened by a heat treatment specialist.^{11 }Reliability, accuracy and validity were augmented through strict control of carburising conditions by the heat treatment specialist.^{11 }Treated samples were prepared by a metallurgist for metallographic examination.^{12, 16, 6}40 measurements of case depth were taken for each sample on a metallurgical microscope using an eyepiece graticule at 50X magnification.^{12}Validity and accuracy were ensured by calibrating the microscope prior to use.^{12}Data AnalysisData was cleansed using methods outlined by Sharma, R (2020). Experimental uncertainty was estimated by determining the greatest difference between the mean and individual measurements for each sample (Max(x

_{1}–))_{mean}^{17}.Scatter graphs and linear models were produced for mean data from each case hardening technique, enabling comparison between two numeric variables.

^{18}Mean case depth values were additionally graphed against the square root of carburising time, linearising the expected model.^{19}The R-squared (R^{2}) value, correlation coefficient (r) and standard error of the estimate (SEE) were determined for each model.^{20, 21}To quantitatively test

Hypothesis 1, two-tailed independentt-tests were conducted to determine whether the difference in means between case depths for successive carburising times were statistically significant.^{21, 22, 23}This specifict-test was selected as it compares the means of two continuous variables.^{11, 12}Ap-value <0.05 was used to accept statistical significance of the difference of means.^{11, 12 }The relationship between case depth and carburising time was deemed to be statistically significant if the difference in means was found to be significant, rejectingNull Hypothesis 1.^{22, 23}To quantitatively testHypothesis 2, differences in mean case depths were compared across each case hardening technique using two-tailed independentt-tests.^{22, 23}If the majority of the differences in means were significant, the difference in case depth across case hardening techniques was deemed significant, refutingNull Hypothesis 2.^{21, 22, 23}RESULTSSummary StatisticsTable 1shows mean case depth produced for each designated carburising time and case hardening method, including estimated uncertainty. The greatest estimated uncertainty is ±0.14mm. 1.96 standard deviations (1.96σ) describes the spread of the middle 95% of the data from the mean value. Sample size was identical for each sample.Sample HistogramGraphs and Models for Empirical DataGraphs produced for pack carburising and gas carbonitriding appear to coincide with the expected relationship (see

Figure 2). Graphsfor cyaniding demonstrate a linear relationship between carburising time and case depth.Difference in Mean TablesThe difference in means between case depth for successive carburising times was found to be statistically significant (see

Table 3).Comparing mean case depth across each case hardening technique demonstrated that majority of the compared means were statistically significant (see

Table 4).DISCUSSIONAnswering Research Question Section 1Results demonstrated that case depth increases as carburising time increases. For pack carburising, the linearised model

(Figure 2b)indicated strong correlation between carburising time and case depth, whereby r = 0.89.^{24}Strong correlation was observed in the linearised model(Figure 2d)for gas carbonitriding, yielding r = 0.96.^{1}A linear model(Figure 2e)fitted data for cyaniding with the strongest correlation, producing a very strong correlation of r = 0.99.^{24}A statistically significant relationship between carburising time and case depth was found for each case hardening technique through testingHypothesis 1.^{23}Taking all evidence into account,Null Hypothesis 1is refuted and statistical significance of the relationship between carburising time and case depth is confirmed. Significance of these relationships imply that case depth can be accurately predicted for select carburising times.The observed relationship between carburising time and case depth coincides with case hardening theory. In accordance to diffusion theory, increasing time given for carburisation/carbonitriding causes an increase in the amount of diffused carbon/nitrogen in the steel, subsequently increasing case depth.

^{6, 7}Answering Research Question Section 2Through testing

Hypothesis 2, difference in case depth between case hardening techniques was found to be significant for typical carburising times, as the majority of the case depths compared across case hardening methods were significant.^{23}Maximum achieved case depth (carburising time 5hrs) was in order of greatest to least: pack carburising, gas carbonitriding, cyaniding. Comparing graphs across case hardening methods revealed that relationships between variables was unique for each technique.Figure 2a(pack carburising) indicated a definite plateau in case depth between the 3hr, 4hr and 5hr carburising times. A plateau of this degree was not observed qualitatively in gas carbonitriding and cyaniding graphs.Figure 2e(cyaniding) demonstrated a linear relationship between variables unlike the other graphs. Taking all evidence into account,Null Hypothesis 2is refuted and the significance in the difference in case depth between each of the case hardening techniques is confirmed.The differences in relationships across case hardening methods corresponds with expectations from theory. In pack carburising, carbon potential is not replenished as carbon diffuses into the steel.

^{6, 7}Thus, quantities of carbon available for absorption into the steel decreases, resulting in actual case depth values deviating from the expected d = ϕ√t model.^{6}In gas carbonitriding, hardening element concentrations are maintained more effectively, enabling carbon/nitrogen diffusion consistent with d = ϕ√t^{6, 7}Despite expectations that the relationship for cyaniding coincides with the model d = ϕ√t due to effectively maintained hardening element concentrations,Figure 2esuggested the relationship was linear. The apparent linear relationship may result from high quantities of absorbed nitrogen in the steel impacting the expected nature for hardening element diffusion, subsequently influencing case depth.Evaluating ReliabilityStandard deviations (95% CI) were used to evaluate consistency of measurements. The largest standard deviations (as percentages of the mean) for pack carburising, gas carbonitriding and cyaniding measurements were 2.91%, 15.6% and 10.1% respectively. Despite poorer consistency for gas carbonitriding and cyaniding, reliability is considered sufficient for the investigation as both Research Questions were successfully addressed. Adequate consistency of results identifies that strict measures taken by the heat treatment specialist and metallurgist to reduce random errors in the Methodology were effective.

Evaluating AccuracyAccuracy was estimated by considering uncertainty of measurements and SEE (95% CI) for the mathematical models. The greatest experimental uncertainty (calculated via Max(x

_{1}–)) across all data was 10.6% (±0.14mm). Qualitatively, pack carburising and gas carbonitriding graphs appeared to correspond with the expected relationship._{mean}Figure 2bandFigure 2ddemonstrated a SEE of ±0.36 and ±0.25 respectively, presenting a small error margin for each model. The SEE forFigure 2ewas ±0.052 demonstrating exceptional accuracy. AlthoughFigure 2eappeared linear (unlike the expected model), it is unlikely that systematic errors caused this. Although uncertainty was significant, accuracy is considered to be sufficient for addressing both Research Questions as the SEE for each graph was minor, and most graphs qualitatively fit expectations.As measurements and models demonstrated accuracy, it is decided that the measures taken by the heat treatment specialist and metallurgist were adequate in reducing systematic errors.

Evaluating ValidityThe results enabled successful testing of

Hypothesis 1andHypothesis 2as per the intention of the investigation. Methodologies for data analysis are considered valid, as the analysis process was supported extensively by academic resources. Successful confirmation of reliability and accuracy provided evidence of the sufficient control measures taken by the heat treatment specialist and metallurgist in experimentation and data collection. The investigation is considered to be sufficiently valid.

Not being able to confirm similar results for other steel grades limited the investigation. Available time and resources limited the range of carburising times and case hardening techniques explored. The inability to perform statistical tests to compare each model to the expected model limited the extent of data analysis.Limitations &Recommendations for Future InvestigationIt is recommended that further testing is conducted into the relationship between carburising time and case depth for a broader range of steel grades. It is also recommended that models produced for each case hardening technique are statistically tested.

CONCLUSIONThe investigation successfully addressed both Research Questions and Hypotheses by the collection and analysis of quantitative data through first-hand experimentation.

Through testing

Hypothesis 1, a statistically significant relationship between total carburising time and case depth in steel has been determined for pack carburising, gas carbonitriding and cyaniding. Results demonstrated that as carburising time increases, case depth increases. Thus,Null Hypothesis 1is refuted, andHypothesis 1is supported.Through testing

Hypothesis 2, the difference in total case depth between each case hardening technique is determined to be statistically significant for typical carburising times, whereby maximum achieved case depth for each technique (carburising time 5hrs) is in order of greatest to least: pack carburising, gas carbonitriding, cyaniding. Graphs for pack carburising deviated moderately from the expected relationship. Qualitatively, gas carbonitriding graphs corresponded to the expected model, while cyaniding graphs appeared linear. Thus,Null Hypothesis 2is refuted, andHypothesis 2is supported. Through evaluation of results, strict control measures taken by the heat treatment specialist and metallurgist during experimentation were found to be sufficient in reducing random and systematic errors. Data collected was successfully analysed to fulfil the requirements of both Research Questions, indicating validity of the methodology. The results and methodology were deemed to be sufficiently reliable, accurate and valid for this investigation. It is recommended that relationships between carburising time and case depth are investigated for a wider range of case hardening techniques and carburising times.REFERENCES

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