In this module, you shall learn about:
Reference documents,
General tips on document navigation,
Important terms & definitions
In this module, you shall learn about:
In a nutshell, an API 510 Pressure Vessel Inspector should know about:
The API 510 Pressure Vessel Inspector examination has two sets of references as study materials:
One set contains ASME codes (Section VIII (Pressure Vessels); Section IX (Welding), and Section V (Non-destructive Testing)).
The second set of study materials or reference documents mostly contain the recommended practices:
API RP 572 (Inspection of Pressure Vessels); API RP 576 (Pressure-Relieving Devices); API RP 571 (Damage Mechanisms); API RP 577 (Welding Inspection); API RP 578 (PMI); PCC-2 (Repair) and finally, the all-important API 510 (Pressure Vessel Inspection Code).
Most of questions from these codes are in open book part of the examination and of calculation type.
You need not memorize them but should know where to look for when solving the open book questions. This is especially important because the search button is disabled during the exam.
You should also how to navigate through these codes and recommended practices during open book part.
When reading a code, don’t immediately dive into the details. Get the bigger picture.
First, understand what the code covers by reviewing the opening paragraphs of each code. This is generally called the Scope or Introduction.
Next, look at the table of contents to understand how the code is structured. This step is often overlooked, and the inspector fails to get the scenario or the purpose of the code.
The closed book exam questions coming from codes and recommended practices are the ones that an inspector would expect to be using on daily basis and therefore, you need to memorize them. These are called practical type of questions.
But don’t worry, we shall supply you with enough presentation, mock question and flash cards to ensure you would not forget them during the exam.
Please note that only API 510 is an inspection code (mandatory), while the rest of API documents are recommended practices (good engineering practice).
Closed book questions mostly come from API 510 code and RPs because this information is supposed to be used by inspectors on daily basis.
For open book questions that need referring to tables, graphs and formulas, you shall have access to both the API RPs and API 510 code besides ASME codes.
We shall cover them within the next 8 modules combined with flash cards and mock exams.
We shall cover them within the next 8 modules combined with flash cards and mock exams.
Codes are based on scientific conclusions while recommended practices are mostly the result of past experience gathered over the years showing the trends and good practices.
That’s why; you may observe that most of the formulas brought within RPs are empirical. The empirical formulas have no sound scientific backing and are merely formulated to show the trends and relationship between various parameters.
Why? Because, to turn an empirical formula into a scientific formula necessitates including many more parameters of less importance and this would unnecessarily complicate the equation whereas empirical formulas are like rule of thumbs and can be of everyday use especially when you do not need to be that accurate.
The analogy would be the difference between a WPS and a Welding Instruction. The welder does not need to know about all the essential and non-essential parameters or the PQR and its associated test reports. All the welder needs to know is the range of amperage & voltage, the welding speed, the type and size of electrode, the welding position, the number of passes and if any pre heat required.
Empirical formulas are used when a very high accuracy is not important. They are basically the mathematical representation of trends.
For example, as a rule of thumb, you need to preheat 4″ or 4t from each side of the weld whichever is more. You do not really need complicated formulas to come to the right number that you cannot even implement in practice.
Scientific formulas accurately explain the phenomena for all ranges of parameters while an empirical formula only works within a limited range.
Overall, the Codes are engineering based while RPs are experience based.
Before going to the relevant section, you need to know which document you need to look at in order to find a particular topic. Therefore, you need to know what is covered in each code and recommended practice.
If you are in doubt, look at the table of contents. If it does not help, look at the list of figures or tables for large volume codes, it shall give you an idea where you can find the topic. For smaller documents, peruse through table of contents or figures.
Try reading the PDF format of documents on a laptop so your eyes and mindset gets used to them. It seems, the brain works differently when you are looking at a hard copy of a document than when you peruse through soft copy of the same document.
Reading soft copies of reference documents help acclimatize yourself while searching for a topic. A little practice is necessary to get it right. It is particularly useful for bigger codes such as ASME Sec V, VIII & IX.
Also try memorizing the topics of codes and RPs so you know where to look for. If you can’t find the relevant section after a couple of minutes, flag off the question and note the question number on a piece of paper as there is a high chance that you shall find it when looking for answers for other questions. Once found, you can go back to the flagged off question and solve it within seconds.
API 510 and API RP 572, 571, 577, 576 should not be a problem navigating as they are much smaller compared to ASME codes. There is also the content list available for each RP.
Please note that the reference codes and RPs provided during the open book part of the exam are not word searchable, hence, you should know where to find each topic.
In the following modules, we shall present the list of important topics and tables complemented with flash cards and mock exams for your practice.
This should help you get an idea where to look for. Fortunately, the list is not exhaustive, so, you should not find much of the problem navigating through the documents.
The followings are the important vocabulary for API 510 course explained in simple language. It not only helps you understand a few basic concepts, but some of these key words and their meaning may also be used as exam questions. Please note that the list in not exhaustive but it intends to explain important key words, their concepts and differences.
In case of conflict between reference documents such as code, recommended practice, standard, project specification, procedure, purchase order, etc., there shall be an order of precedence when one document over rules or vetoes another reference document.
Obviously, if API RP 510 is more stringent or more onerous than a regulation, this means, it is not in conflict with a regulation but is over and above that regulation.
Repair means the work necessary to restore the vessel that can be operated safely at its original operating pressure and temperature.
Alteration means repairing the vessel such that it changes it’s original operating pressure and/or temperature range (integrity operating window).
So, any repair such as replacement of parts with same or similar parts (like for like) and any restoration work are called a ‘’repair’’ as long as it’s current allowable operating pressure and temperature (Maximum allowable working pressure (MAWP) and minimum design metal temperature (MDMT) does not change.
On the other hand, any activity that changes any of these parameters (MAWP, MDMT, IOW), it is termed as alteration.
Any restorative work that results to a change in MAWP, MDMT and subsequent rerating.
Rerating may be either upgrading (increase in allowable MAWP and decrease in MDMT) or downgrading (decrease in MAWP or increase in MDMT).
If re-rating leads to downgrading, then it is called de-rating which means demoting.
Please note that an increase in MAWP is an upgrade because the vessel can tolerate higher working pressure like a car that can go at a higher speed which is understandable.
But a decrease (and not an increase) in MDMT is an upgrade because the lower the MDMT, the larger, the operating window.
For example, a vessel that can operate at 10 F is superior and more versatile than a vessel that operates at 20 F.
Remember, both rerating and de-rating results in a change in MDMT and/or MAWP and hence it is termed as an alteration and not a repair.
Alteration requires a pressure test unless exempted in writing by both the engineer and inspector.
Repair does not normally require a pressure test unless specifically asked by the inspector or engineer.
Examination specifically means QC activities such as an NDT activity. It is not an inspection.
The closest analogy could be the difference between a laboratory blood test (examination) and doctor’s diagnosis (Inspection which includes evaluation and interpretation or acceptance/rejection). Examination reports shall be approved by the inspector.
NDT technician examines the material by an NDT method and reports the result.
NDT examiner can also report the acceptance or rejection of a material or equipment against an approved acceptance criteria if authorized by the inspector.
A. Code calculation questions will be oriented toward existing pressure vessels, not new pressure vessels.
API Authorized Pressure Vessel Inspectors should be able to check and perform calculations relative to in-service deterioration, repairs, rerates, or alterations. Only internal pressure loadings will be considered for the API 510 examination.
Note: Candidates are expected to understand the US customary units (inches, feet, PSI, etc.) and the SI units (metric system) and to use both system formulas.
The following categories describe the minimum necessary knowledge and skills:
The Inspector should be able to take inspection data and determine the internal and external inspection intervals.
The Inspector must be able to calculate:
a) Metal Loss (including corrosion averaging) (API 510, 7.4)
b) Corrosion Rates (API 510, 7.1)
c) Remaining Corrosion Allowance (API 510, 7.1)
Remaining Corrosion Allowance = tactual – trequired
d) Remaining Service Life (API 510, 7.2)
e) Inspection Interval (API 510, Section 6)
The formulas for performing the above calculations and rules for setting the inspection intervals may be “closed-book” during the examination.
The inspector must be able to determine the joint efficiency “E” of a vessel weld. Inspector should be able to determine:
a) Weld Joint Categories (ASME Section VIII, UW-3);
b) Type of radiography (full, spot, or none) performed basis the nameplate markings (RT-1, RT-2, etc.); (UW-11)
c) Joint efficiency by reading Table UW-12;
d) Joint efficiency for seamless heads and vessels sections per UW-12(d); and
e) Joint efficiency for welded pipe and tubing per UW-12(e).
Determining joint efficiency may be part of the internal pressure problem since joint efficiency “E” is used in the formulas for determining required thickness or Vessel Part MAWP.
The inspector must be able to compensate for the pressure resulting from static head. All static head will be based upon a Specific Gravity of 1.0. The inspector should be able to:
a) List the static head/pressure conversion factor (0.433 psi/ft);
b) Know the difference between vessel MAWP and vessel part MAWP (ASME Section VIII, UG-98)
c) Calculate static head pressure on any vessel part;
d) Calculate total pressure (MAWP + static head) on any vessel part;
e) Calculate maximum vessel MAWP given vessel parts MAWP and elevations
Static head calculations may also be required during the internal pressure calculations if static head data is given in the examination problem.
The inspector should be able to determine:
a) The required thickness of a cylindrical shell based on circumferential stress given a pressure (UG-27(c)(1));
b) The required thickness of a spherical shell based on circumferential stress given a pressure (UG-27(d))
c) The vessel part MAWP for a cylindrical shell based on circumferential stress given a metal thickness (UG27(c)(1));
d) The required thickness of a head (ellipsoidal, and hemispherical) given a pressure. (UG-32(c), and (e))
e) The vessel part MAWP for a head (ellipsoidal, and hemispherical) given a metal thickness. (UG-32(c), and (e)).
f) Whether a head (ellipsoidal or hemispherical) meets Code requirements given both pressure and metal thickness. (UG 32(c) and (e)).
The inspector should also be able to compensate for the corrosion allowance: add or subtract based on requirements of the examination problem. The Section VIII, Appendix 1 formula for cylinders, which is based on outside diameter, can be used.
The Appendix 1 formulas for non-standard heads will not be required.
The inspector should be knowledgeable of the rules for design of shells and tubes under external pressure (UG-28). The inspector will not be required to perform external pressure calculations.
The inspector should be able to:
a) Calculate a test pressure compensating for temperature. (UG-99 and UG-100)
b) Be familiar with the precautions associated with hydrostatic and pneumatic testing, such as minimum test temperatures, protection against overpressure etc.
c) Be familiar with all steps in a hydrotest procedure (UG-99 and UG-100)
d) Be familiar with all steps in a pneumatic test procedure (UG-100 and UG-102)
a) The inspector should understand impact testing requirements and impact testing procedure (UG-84)
b) The inspector should be able to determine the minimum metal temperature of a material which is exempt from impact testing (UG-20(f), UCS-66, UCS-68(c))
The inspector must be able to determine if weld sizes meet Code requirements. The inspector should be able to:
a) Convert a fillet weld throat dimension to leg dimension or vice versa, using conversion factor (0.7); and
b) Determine the required size of welds at opening (UW-16)
The inspector should understand the key concepts of reinforcement, such as replacement of strength removed and limits of reinforcement.
B. The following are typical ASME code engineering requirements that API certification candidates will NOT be expected to know for purposes of the certification examination.
1. Required thickness calculations for wind, earthquake, and other secondary stress loadings;
2. Supplementary design formulas and calculations for non-cylindrical shell components;
3. External pressure calculations (but should understand the rules governing external pressure noted in Section 5);
4. Nozzle calculations for external loads;
5. Flange calculations;
6. Brazing requirements;
7. Ligament calculations;
8. Stayed flat heads and sizing of stays;
9. Tubesheet calculations (stayed or unstayed) and tube to tubesheet joints and loads;
10. Relief valve sizing;
11. Lifting lug and other structural type calculations;
12. Proof testing requirements;
13. Required inspections for new construction, except as they apply to alterations and repairs;
14. Zick analysis;
15. Integrally forged pressure components;
16. Cryogenic vessels (below -50°F);
17. Dimpled, embossed, jacketed, and non-metallic vessels and assemblies;
18. NDE requirements for acoustic emission, eddy current, and motion radiography;
19. ASME Sections UF, UB, UNF, UHA, UCI, UCL, UCD, UHT, ULW, ULT, UHX and UIG;
20. Code Cases and interpretations;
21. Requirements for pressure vessels for human occupancy; and
22. Rules for natural resource vessels, API 510, Section 9.
The inspector should have the knowledge and skills required to review a Procedure Qualification Record, a Welding Procedure Specification, and a Welder Performance Qualification to be able to determine the following:
a) Determine if procedure and qualification records are in compliance with applicable ASME Boiler and Pressure Vessel Code and any additional requirements of API 510.
The weld procedure review will include:
• Weld Procedure Specification (WPS)
• Procedure Qualification Record (PQR)
• Welder Performance Qualification (WPQ)
b) Determine if all required essential and non-essential variables have been properly addressed. (Supplemental essential variables will not be a part of the WPS/PQR)
c) Determine that the number and type of mechanical tests that are listed on PQR are the proper tests, and whether the results are acceptable.
d) Determine that the welder is qualified to make a production weld according to the WPS
WELD PROCEDURE REVIEW WILL ONLY INCLUDE SMAW, GTAW, GMAW, OR SAW, with the following limitations:
a) No more than one process will be included on a single WPS,PQR or WPQ and the WPS to be reviewed will be supported by a single PQR.
b) Filler metals will be limited to one-per-process for SMAW, GTAW, GMAW, or SAW
c) The PQR will be the supporting PQR for the WPS.
d) The WPQ test coupon is to be welded in accordance with a qualified WPS.
e) Base metals will be limited to P-No. 1, P-No. 3, P-No. 4, P-No. 5, and P-No. 8.
f) Dissimilar base metal joints, and dissimilar thicknesses of base metals will be excluded.
g) Special weld processes such as corrosion-resistant weld metal overlay, hard-facing overlay, and dissimilar metal welds with buttering of ferritic member will be excluded.
h) For P-No. 1, P-No. 3, P-No. 4, and P-No. 5, for the purpose of the examination the lower transition temperature will be 1330°F and the upper transformation temperature will be 1600°F.
1. ASME Section VIII, Div. 1
The inspector should be familiar with and understand the general rules for welding in ASME Section VIII, Div. 1, Parts UW and UCS such as:
a) Typical joints and definitions
b) Weld sizes
c) Restrictions on joints
d) Maximum allowable reinforcement
e) Inspection requirements
f) Heat treatment
2. API 510 The inspector should be familiar with and understand any rules for welding in API 510. Any rules for welding given in API 510 shall take precedence over those covering the same areas in ASME, Section VIII, Div. 1.
3. “Editorial” and non-technical requirements for the welding subject matter, the candidate is to be tested on, are excluded.
This includes items such as the revision level of the WPS, company name, WPS number and date, and name of testing lab. However, the API 510 applicants shall know that the PQR and WPQ must be certified by signing and dating.
API RP 577: The inspector shall be familiar with all the requirements of and information in API RP 577.
ASME Section V, Nondestructive Examination
NOTE: The examination will cover ONLY the main body of each referenced Article, except as noted.
A. Article 1, General Requirements: The inspector should be familiar with and understand;
1. The Scope of Section V,
2. Rules for use of Section V as a referenced Code,
3. Responsibilities of the Owner / User, and of subcontractors,
4. Calibration,
5. Definitions of “inspection” and examination”,
6. Record keeping requirements.
B. Article 2, Radiographic Examination:
The inspector should be familiar with and understand;
1. The Scope of Article 2 and general requirements,
2. The rules for radiography as typically applied on pressure vessels such as, but not limited to:
a) Required marking
b) Type, selection, number, and placement of IQI’s,
c) Allowable density
d) Control of backscatter radiation
e) Location markers
3. Records
C. Article 6, Liquid Penetrant Examination, including Mandatory Appendices II and III: The inspector should be familiar with and understand:
1. The Scope of Article 6,
2. The general rules for applying and using the liquid penetrant method such as, but not limited to;
a) Procedures
b) Contaminants
c) Techniques
d) Examination
e) Interpretation
f) Documentation and
g) Record keeping
D. Article 7, Magnetic Particle Examination (Yoke and Prod techniques only): The inspector should be familiar with and
understand the general rules for applying and using the magnetic particle method such as, but not limited to;
1. The Scope of Article 7,
2. General requirements such as but not limited to requirements for:
a. Procedures
b. Techniques (Yoke and Prod only)
c. Calibration
d. Examination
e. Interpretation
f. Documentation and record keeping
E. Article 23, Ultrasonic Standards, Section SE–797 only – Standard practice for measuring thickness by manual ultrasonic pulse-echo contact method: The inspector should be familiar with and understand;
1. The Scope of Article 23, SE-797,
2. The general rules for applying and using the Ultrasonic method
3. The specific procedures for Ultrasonic thickness measurement as contained in paragraph 7.
ASME Section VIII, Div. 1 and API 510. General nondestructive examination requirements: ASME Section VIII, Div.
The inspector should be familiar with and understand the general rules for NDE (UG, UW, Appendices 4, 6, 8, and 12)
API 510: The inspector should be familiar with and understand the general rules for NDE in API 510.
The following topics may be covered in the examination. More information relative to each of the categories is contained in section.
1. Organization and Certification Requirements.
2. Types and Definitions of Maintenance Inspections.
3. Types of Process Corrosion and Deterioration.
4. Modes of Mechanical, Thermal, and High Temperature Deterioration.
5. Pressure Vessel Materials and Fabrication Problems.
6. Welding on Pressure Vessels.
7. Nondestructive Examination (NDE) Methods.
8. Corrosion and Minimum Thickness Evaluation.
9. Estimated Remaining Life.
10. Inspection Interval Determination and Issues Affecting Intervals.
11. Relief Devices.
12. Maintenance Inspection Safety Practices.
13. Inspection Records and Reports.
14. Repairs/Alterations to Pressure Vessels.
15. Rerating Pressure Vessels.
16. Pressure Testing After Repairs, Alterations, or Rerating
API 510, Pressure Vessel Inspection Code
All of API 510 is applicable to the examination unless specifically excluded. For example: Section 9 and Appendix E are excluded.
ATTN: Test questions will be based on the following portions of the document only:
Section 2 Terms and Definitions
3.3 Amine Stress Corrosion Cracking
3.8 Atmospheric Corrosion
3.11 Brittle Fracture
3.14 Caustic Corrosion
3.15 Caustic Stress Corrosion Cracking
3.17 Chloride Stress Corrosion Cracking
3.20 Cooling Water Corrosion
3.22 Corrosion Under Insulation (CUI)
3.27 Erosion/Erosion-Corrosion
3.36 High Temperature Hydrogen Attack
3.37 Hydrochloric Acid Corrosion
3.43 Mechanical Fatigue (including Vibration-induced Fatigue)
3.58 Sour Water Corrosion
3.61 Sulfidation
3.67 Wet H2S Damage (Blistering/HIC/SOHIC/SCC)
Entire document is subject to testing, including Annex B. All other Annexes are not subject to testing.
Entire document is subject to testing with the exception of annexes.
Entire document is subject to testing
Entire document is subject to testing
ATTN: Test questions will be based on the following portions of the document only:
Article 201: Butt-Welded Insert Plates in Pressure Components
Article 202: External Weld Buildup to Repair Internal Thinning
Article 209: Alternatives to Postweld Heat Treatment
Article 210: In-Service Welding Onto Carbon Steel Pressure Components or Pipelines
Article 211: Weld Buildup, Weld Overlay, and Clad Restoration
Article 212: Fillet Welded Patches
Article 215: Repair Welding Considerations for Cr-Mo Steel Pressure Vessels
Article 216: Welded Hot Taps in Pressure Equipment or Pipelines
Article 304: Flaw Excavation and Weld Repair
Article 305: Flange Repair and Conversion
Article 312: Inspection and Repair of Shell and Tube Heat Exchangers
Article 501: Pressure and Tightness of Piping and Equipment
Article 502: Nondestructive Examination in Lieu of Pressure Testing for Repairs and Alternations
is the visual inspection from outside the vessel (maximum interval 5 years).
On stream inspection means external inspection of vessel using an NDT technique.
The difference between external inspection and on-stream inspection is that in external inspection, only visual inspection is carried out while on-service inspection involves the NDT examination as well.
Also, external inspection is aimed at detecting the environmental corrosion while on-stream inspection is aimed at substituting internal inspection, that is, when it is possible to get the same necessary information and examination by on-stream inspection without opening the vessel up for internal inspection.
On-Stream or In- service inspection could replace periodic internal inspection if approved by the inspector and owner, provided it gives the same required information as internal inspection.
External inspection could not replace internal inspection while On Stream Inspection can replace internal inspection subject to terms and conditions.
Inspection from inside of vessel both visually and with NDT methods with a maximum interval of 10 years or half corrosion life which ever happens sooner.
Precision and accuracy are often used interchangeably, but in science they have very different meanings. Measurements that are close to the known value are said to be accurate, whereas measurements that are close to each other are said to be precise.
Accuracy is used for calibration purpose to determine how accurate the readings are with respect to a known value.
The point of measurement normally means a circular area with a diameter of 3’’.
API does not differentiate between owner and user. The owner/user is responsible for inspection and repair to meet the code.
This makes sense because if owner and user were differentiated as two separate legal entities, then, none of them could be hold them accountable because the owner would say that the user was supposed to comply with jurisdictional requirements while the user would argue that that the pressure vessel belongs to owner who should be held accountable.
Owner/user is accountable for any shortcoming and non compliance to codes and specifications or jurisdictional requirements.
API 510 requires that an owner/user shall employ or subcontract an inspection organization (or an inspection program and authorized inspector), a repair organization, an engineer, and examiner. Please note that the ultimate responsibility lies with the owner/user while other individuals are accountable to the owner/user within their scope of responsibilities.
Inspector means authorized API 510 pressure vessel inspector.
The inspector is responsible to the owner for inspection and approval of the vessel for continued safe operation.
The inspector can be an individual working for the government/jurisdiction, an insurance company, for a third party under contract with the owner/user or directly working for the owner/user.
The NDT examiner is responsible for performing NDT activities as per approved procedure and if authorized by the inspector, can also prepare the acceptance and rejection part of the report.
However, please note that the Inspector is the final authority in accepting or rejecting the NDT reports as well as all the inspection records.
Certification of the NDT examiner shall be maintained by his/her employer and shall be available for inspector’s review.
The pressure vessel engineer is an individual or a team who is knowledgeable in the design, review, analysis and evaluation of pressure vessels and is appointed by the owner/user.
This is the pressure range and temperature range that the pressure vessel is allowed to work. The range is determined by design premises and depends on the type of material and its thickness.
Exceeding the IOW range may affect the integrity of the vessel. There could be other parameters within IOW such as process fluid, velocity, but MAWP and MDMT are the most prominent.
Any change in the process equipment or material or hardware shall be documented. It shall be determined whether such changes may affect vessel integrity (say, by increasing the corrosion rate or change in damage mechanism).
Relevant personnel such as the Engineer, corrosion specialist, inspector, examiner and maintenance personnel may be involved to cascade down or reflect such changes in inspection planning, repair and maintenance.
Points or areas on the pressure vessel are identified that normally expect to have the highest corrosion rate or stress concentration. These areas are inspected and examined periodically to assess the vessel condition.
The CML locations are selected to be representative of corrosion behavior of the vessel. It makes sense to select those points or areas where maximum corrosion or damage is expected.
The inspector selects the monitoring locations based on previous history of inspection, damages occurred on similar vessels under similar operating and environmental conditions and may seek corrosion specialist opinion on expected damage mechanisms for a particular vessel.
Quality assurance is the design and planning of quality control activities to ensure that the service or equipment has met certain requirements while the Quality Control is the implementation of those control activities in order to demonstrate or verify that the requirements are met.
Not all parts or components of the pressure vessel have equal value or effect on the integrity of equipment. Similarly, not all equipment has equal value or effect on the integrity of a plant.
It is also important to understand what the consequence of failure for a particular part or equipment would be.
Risk-based inspection considers both the probability of failure and consequence of failure.
Once, we know what the probability and consequence of failure are, inspection efforts can be directed towards more critical parts, locations, parts and equipment thereby reducing the probability of failure, downtime and inspection costs while increasing equipment reliability, equipment availability and safety.
There might be a situation when the probability of failure is low, but the consequences of failure are huge and catastrophic in terms of cost, downtime or even human lives. In such situations, the overall risk is still high.
Remember that the owner/user is ultimately responsible for preparing, documenting, executing, and assessing pressure vessel/pressure-relieving device inspection and repair.
Owner/User shall have QA system that shall include:
As you can see, this is more or less, a list of ISO 9001 requirements.
Remember that embrittlement is the reverse of ductility.
Toughness is the resistance of the material to deform under force/stress.
Toughness is quantitatively the area under the stress strain curve.
Toughness depends both on amount of stress it can tolerate, and it’s amount of elongation.
Hardness is the resistance of material against penetration or indentation.