National Academies Press: OpenBook
« Previous: Chapter 1 - Background
Page 8
Suggested Citation:"Chapter 2 - Research Approach." National Academies of Sciences, Engineering, and Medicine. 2019. Acceptance Criteria of Complete Joint Penetration Steel Bridge Welds Evaluated Using Enhanced Ultrasonic Methods. Washington, DC: The National Academies Press. doi: 10.17226/25494.
×
Page 8
Page 9
Suggested Citation:"Chapter 2 - Research Approach." National Academies of Sciences, Engineering, and Medicine. 2019. Acceptance Criteria of Complete Joint Penetration Steel Bridge Welds Evaluated Using Enhanced Ultrasonic Methods. Washington, DC: The National Academies Press. doi: 10.17226/25494.
×
Page 9
Page 10
Suggested Citation:"Chapter 2 - Research Approach." National Academies of Sciences, Engineering, and Medicine. 2019. Acceptance Criteria of Complete Joint Penetration Steel Bridge Welds Evaluated Using Enhanced Ultrasonic Methods. Washington, DC: The National Academies Press. doi: 10.17226/25494.
×
Page 10
Page 11
Suggested Citation:"Chapter 2 - Research Approach." National Academies of Sciences, Engineering, and Medicine. 2019. Acceptance Criteria of Complete Joint Penetration Steel Bridge Welds Evaluated Using Enhanced Ultrasonic Methods. Washington, DC: The National Academies Press. doi: 10.17226/25494.
×
Page 11
Page 12
Suggested Citation:"Chapter 2 - Research Approach." National Academies of Sciences, Engineering, and Medicine. 2019. Acceptance Criteria of Complete Joint Penetration Steel Bridge Welds Evaluated Using Enhanced Ultrasonic Methods. Washington, DC: The National Academies Press. doi: 10.17226/25494.
×
Page 12
Page 13
Suggested Citation:"Chapter 2 - Research Approach." National Academies of Sciences, Engineering, and Medicine. 2019. Acceptance Criteria of Complete Joint Penetration Steel Bridge Welds Evaluated Using Enhanced Ultrasonic Methods. Washington, DC: The National Academies Press. doi: 10.17226/25494.
×
Page 13

Below is the uncorrected machine-read text of this chapter, intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text of each book. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

8 Research Approach 2.1 Summary of the State of the Practice 2.1.1 Current AWS D1.5 Requirements A set of acceptance criteria provides a measure or refer- ence by which a standard of quality is applied to provide ade- quate structural performance. One definition of acceptance criteria is “a set of rules formulated in terms of the require- ments to NDE recorded parameter values for judgement of whether flaws are acceptable or rejectable [7].” It would be ideal for acceptance criteria to reject and repair all imperfec- tions which could be harmful to the structure while accepting all harmless imperfections, but this idea is unattainable in a rational weld acceptance criteria. If one takes into account the economic considerations of repairing a fatigue failure due to undersizing a flaw compared to the cost of repairing a benign imperfection, it may be found that the acceptance criteria needs to be set so that many harmless imperfections may need to be repaired in order to eliminate one harmful imperfection [8]. On a very broad level, all acceptance criteria can be placed into one of two categories: workmanship criteria or fitness- for-service (fracture-mechanics-based) criteria. Workman- ship criteria are based on a general, arbitrary control on the level of quality [3] and is aimed at ensuring that an acceptable workmanship level is met [7]. Many welding codes employ a workmanship criteria, including AWS D1.1 Structural Weld- ing Code [9] and AWS D1.5 Bridge Welding Code. Generally speaking, although workmanship criteria have historically provided adequate performance, they are often based on experience and do not give an objective comparison to the actual size that would result in component failure. Further, the apparent “success” of workmanship criteria (i.e., the observa- tion that no problems mean that the criteria are working) may not necessarily be due to the criteria themselves, but due to a series of factors that are unknown or unaccounted for since the criteria were arbitrarily crafted. Fitness-for-service (FFS) criteria, also known as Engineer- ing Critical Assessment (ECA), are based on fracture mechan- ics which uses information on member loading and material properties to determine an acceptable initial discontinuity size for the intended service life. FFS will typically permit larger discontinuities than workmanship criteria but require accu- rate and reliable measurements of flaw size and location [10]. Further, FFS requires accurate estimates of material properties and residual stresses, in addition to static and cyclic stresses over the service life of the structure. AWS D1.5 conventional UT employs workmanship crite- ria based on the amplitude of the reflected sound along with the flaw length. Conventional UT technicians perform bridge weld testing under the AWS D1.5 code by utilizing a manual raster scanning approach where the probe is rotated and trans- lated on the testing surface to provide coverage of the entire weld volume and to maximize the signal response amplitude. In AWS D1.5, thresholds for flaw rejection using conventional UT were developed through calibration to criteria used tradi- tionally for RT that were not based on structural performance [3, 4]. RT and UT utilize very different approaches for discon- tinuity detection due to the actual physics associated with the technologies. For example, RT responds to changes in density, which are recorded on a 2-D film, while UT measures reflec- tion of sound in both the amplitude and time domain. It cannot be assumed that UT or PAUT can always detect the same discontinuities as RT. Generally, it has been found that UT methods have increased sensitivity to crack-like flaws while RT has increased sensitivity to volumetric flaws. For conventional UT inspections, according to AWS D1.5, the indication rating is determined based on the indication amplitude compared to the reference standard reflector and the sound path distance. Decreasing values (i.e., more negative values) of indication rating are more severe. The indication rating is derived by subtracting the reference gain and an attenuation factor from the equipment gain when the indication amplitude matches the reference amplitude. The C H A P T E R 2

9 attenuation factor is included to account for the ultra- sonic attenuation due to the loss of amplitude as the sound travels through the steel. Discontinuities larger than the reference reflector, which is a 1.5 mm (0.06″) diameter SDH, should reflect more sound than the reference reflec- tor. Therefore, the equipment gain will be lower when the indication amplitude matches the reference level. A nega- tive indication rating would result if the sound traveled the same distance in the inspection as the reference reflector and lower equipment gain is required to match the reference amplitude. Assuming that the sound path remains the same, a positive indication rating would result if more equipment gain is required to match the reference amplitude. Based on the loading (compression or tension), indication rating, plate thickness, and testing angle, the indication is classified by assumed severity: • Class A (large flaws): Any indication in this category is rejected (regardless of length). • Class B (medium flaws): Any indication with a length greater than ¾ inch is rejected. • Class C (small flaws): Any indication in this category with a length greater than 2 inches or ¾ inch for an indi- cation in the top or bottom quarter of a tension weld is rejected. • Class D (minor flaws): Any indication in this category is accepted regardless of length or location in the weld. For plate thicknesses up to 1.5 inches, the range for intermediate classifications (i.e., Class B and Class C) is 1 decibel (dB). Therefore, only 3 dB separates a Class A (automatically rejectable) indication from a Class D (auto- matically acceptable) indication. For plate thicknesses greater than 1.5 inches, the range for intermediate classifi- cations is 2 dB, and 5 dB separates a Class A indication from a Class D indication. AWS D1.5:2015 includes alternate acceptance criteria in Annex K to allow for the implementation of PAUT in lieu of conventional UT for testing of bridge welds. This test- ing procedure employs a line scanning approach where the probe remains perpendicular to the weld at a constant index position. The procedure uses a sectorial focal law which pro- duces a sound wave over a range of incidence angles. This helps to insonify the weld volume. However, multiple scans at varying index points may be necessary for complete cov- erage. The acceptance criteria in Annex K were developed as an adaptation of an existing conventional UT acceptance criteria in AWS D1.1 (Annex Q) and were also workman- ship criteria; amplitude of the reflected sound along with the flaw length form the basis of the acceptance criteria. Simi- larly, Annex K uses the same size reference standard reflector and the same indication classifications (Class A–D). As will be discussed further in Chapter 3, the acceptance criteria in AWS D1.1 Annex Q and subsequently AWS D1.5 Annex K do not match the acceptance criteria in AWS D1.1 or D1.5 Clause 6 for conventional UT. While the classifications and their respective maximum length requirements are very similar for Annex K and conventional UT, the range in inter- mediate classifications (i.e., Class B and Class C) are much larger. Class B has a 5 dB range, and Class C has a 6 dB range. Therefore, 11 dB separates a Class A (automatically rejectable) indication from a Class D (automatically accept- able) indication. For Annex K, the reference amplitude is consistently used as the distinction between a Class B or Class C indication, while the reference amplitude does not correlate to a distinct flaw classification in the conventional UT tables. Instead of using an indication rating and an attenua- tion factor to evaluate the amplitude of the indication such as is performed in Clause 6 conventional UT inspections, PAUT utilizes a calibration method with reference reflectors placed at various depths (i.e., TCG). With this correction, the amplitude measured in percentage of full screen height (%FSH) is compared directly with the reference amplitude. Indications with a greater amplitude in %FSH, therefore, are more severe, unlike conventional UT where more nega- tive indication ratings are more severe. 2.1.2 Comparison to Other UT Codes A collection of reference standard provisions, both national and international, related to ultrasonic testing have been summarized below. Specifically, a comparison of each standard’s policy on acceptance criteria, material attenuation, and probe frequency has been presented in Table 1, Table 2, and Table 3, respectively. The ultrasonic codes included in this summary are as follows: • Canadian Standards Association (CSA) W59 code, appli- cable to bridges [11] • European Standard (EN) and International Organization for Standardization (ISO) codes, applicable to bridges • American Society of Mechanical Engineers (ASME) Boiler and Pressure Vessel Code (BPVC), applicable to the gas and nuclear industry [12] • Japanese Industrial Standard (JIS) Z 3060 code, applicable to bridges [13] 2.1.2.1 Acceptance Criteria Codes that included an acceptance criteria based on mea- suring the flaw size of weld flaws require that the flaw sizing procedures be developed by the PAUT technician and verified

10 Specification Probe Shear Wave Frequency Range (MHz) Notes Conventional UT PAUT AWS D1.5-15 2–2.5 1–6 — CSA W59-18 2–2.5 (Fixed Attenuation) 2.25–10 (TCG) 2.25–10 (TCG) — ISO 17640-17 2–5 No stipulation Lower frequencies may be necessary for testing at long sound paths and/or high material attenuation ASME BPVC-17 1–5 1–5 — JIS Z 3060-15 2–5 2–5 Sound path length stipulations are put on using higher frequencies Table 3. Probe frequency summary. Specification Acceptance criteria based on flaw sizing using PAUT Prescribes flaw sizing procedure Acceptance criteria based on max amplitude & length using PAUT Requires performance qualification AWS D1.5-15 X n/a X CSA W59-18 * X (Flaw Sizing) ISO 19285-17 X ASME BPVC CC 2235-13 X X JIS Z 3060-15 X X X X *CSA W59-18 does not provide any specific acceptance criteria for PAUT based on flaw sizing but gives minimum requirements and allows for other acceptance criteria which have been deemed to be equivalent. Table 1. Acceptance criteria summary. Specification Accounts for the material attenuation due to varying grade or microstructure If so, how? Conventional UT PAUT AWS D1.5-15 No n/a n/a CSA W59-18 No (UT) / yes(PAUT) n/a Qualification testing through same medium. ISO 17640-17 Yes Requires a calibration block. If the calibration block and test object are not acoustically the same, a transfer correction is to be applied. ASME BPVC-17 Yes Requires a calibration block of the same product form and material specification of the material being examined. If any acoustic differences remain between the calibration block and test object, a transfer correction is to be applied. JIS Z 3060-15 Yes Requires all calibration blocks to be of a steel material with equivalent acoustic characteristics to the test object. Table 2. Material attenuation summary.

11 for accuracy through performance qualification of the PAUT procedure on weld mockups representative of those being inspected before performing testing. None of the PAUT codes provide a prescriptive procedure for measuring the through- thickness height of weld flaws. AWS D1.5 Annex K uses maximum amplitude and length for the acceptance criteria for PAUT. It does not require that any performance qualification testing be performed. It out- lines the requirements of performing a mockup verification at the option of the PAUT technician or when required by the engineer. CSA W59 added a TCG approach in the 2018 edition for conventional UT or raster scanned manual PAUT, which is intended to provide an equivalent level of quality as the cur- rent conventional UT acceptance tables but has one table for all angles. These changes were compared to AWS D1.5 Annex K, and it was found that the CSA W59 acceptance cri- teria will generally be conservative compared with the current AWS method [14–16]. The CSA code also provides require- ments for use of encoded line scanned PAUT or other alterna- tive ultrasonic systems in lieu of conventional UT if agreed to in writing by the engineer and contractor prior to inspection. In order to use encoded PAUT, it requires that a written pro- cedure be developed and that performance qualification tests of the procedure be performed to verify that the minimum required sensitivity is provided. No prescriptive procedures are provided for flaw sizing or scanning of the welds. ISO 19285:2017 [17] provides acceptance criteria for PAUT which may be applied to bridge welds. This code allows for either evaluating the welds using the flaw size (e.g., flaw height and length) or maximum amplitude and flaw length. This code requires performance qualification for all PAUT inspec- tion procedures on a test block of the same material and simi- lar thickness as the test object with reflectors of prescribed size and location. No prescriptive procedures are provided for flaw sizing, and verification of flaw sizing procedures is required. ASME BPVC Code Case 2235-13 [18] provides acceptance criteria for PAUT in lieu of RT for the nuclear and petro- chemical industries. The code case allows that evaluation of final acceptance only be performed by flaw sizing, but ampli- tude may be used for detection. The code case requires per- formance qualification of all PAUT inspection procedures on a test block of the same material with multiple reflectors throughout the thickness of the part. Requirements are given for the size and location of the reflectors. No prescriptive pro- cedures are provided for flaw sizing, and verification of flaw sizing procedures is required. JIS Z 3060-2015 does not provide an acceptance criteria specifically for PAUT. This code provides classification of discontinuities based on conventional UT results, but no acceptance criteria is included. 2.1.2.2 Material Attenuation AWS D1.5 Annex K is the only code that does not require PAUT technicians to account for differences in material attenuation between the calibration block and the test spec- imen. In fact, there is no discussion on the acoustic proper- ties of the calibration block compared to the test object in the AWS code. For conventional UT, both the AWS D1.5 and CSA W59 account for attenuation in the test specimen by the application of an attenuation factor and use of an Interna- tional Institute of Welding (IIW)-type reference block to set the reference amplitude. However, the 2018 edition of CSA W59 provides a TCG approach in lieu of the fixed attenua- tion approach for conventional UT, while the TCG approach is required for manual raster scanned PAUT. While there is limited discussion in the CSA code on how to account for differences in material attenuation, it does state that the cali- bration block should be “acoustically equivalent” to the test object. For encoded line-scanned PAUT inspections, the CSA code requires a calibration procedure be developed on a case- by-case basis as part of a written procedure. The ISO and ASME codes specifically state that modifi- cations to calibration are required if the material attenua- tion differs between the calibration block and the test object, including both base metal and weld metal. This is typically in the form of a transfer correction. Methods for determining the transfer correction are described in detail in Section 3.4.2. ISO 17640 [19] requires a transfer correction be applied when a difference of 2 dB to 12 dB is observed at the longest inspection sound path. Any difference less than 2 dB is negligible, and any difference greater than 12 dB is a cause for reevaluation of the calibration procedures. ASME BPVC [12] states that if “the block material is not of the same product form or has not received the same heat treatment, it may be used provided it meets all other block requirements and a transfer correction for acoustical property differences is used.” ASME does not provide requirements on the use of a transfer correction; instead, it is left to an inspector’s discretion. JIS Z 3060 [13] provides five different calibration blocks to be used in different circumstances. Each reference block is required to be of a steel material with equivalent acoustic characteristics to the test object. A single, unanimous definition of the phrases acousti- cally equivalent, acoustic characteristics, or acoustic properties does not exist. ISO [20] defines acoustical properties as the characteristics of a material which control the propagation of sound in a material. In ultrasonic testing, these principal characteristics are ultrasonic velocity and attenuation. For example, ASTM E114 [21] states that “the reference standard material and production material must be acoustically simi- lar (in velocity and attenuation).” JIS Z 3060 states that the difference in the ultrasonic velocity of the test object and the calibration block shall be within ±2% and that the transfer

12 correction shall be within ±2 dB. Measurement of the acous- tic properties requires ultrasonic testing of the test object and calibration block including the use of normal incidence shear wave probes and/or pitch-catch methods. ISO 2400, the stan- dard for the IIW calibration block, imposes strict require- ments on the material, heat treatment, and surface finish of the IIW reference block. Following fabrication with these guidelines, the acoustic velocity of the block must be checked and fall within ±0.2% of the prescribed wave velocities. Ultrasonic velocity and attenuation may be the two material characteristics to have the biggest impact on ultrasonic evalu- ation, but grain size, grain structure, material composition, and surface roughness are all factors determining the velocity and attenuation of a material. 2.1.2.3 Probe Frequency AWS D1.5 and CSA W59 restrict the probe frequency for conventional UT due to the fixed attenuation factor, which is only valid for a specific probe size, shape, and frequency [15]. The 2018 edition of the CSA W59 code allows a wide range of probe frequencies for the TCG approach, but, as noted above, this requires that the calibration block be acoustically equivalent to the test object. The other codes allow a wider range of probe frequencies but also require that a calibration be performed to take into account material attenuation. The ISO 17640 code [19] states that lower frequencies are rec- ommended for conventional UT where acceptance is deter- mined based on maximum amplitude and length rather than flaw characterization and sizing. While removed for the 2017 edition, the 2010 edition of ISO 17640 stated that initial testing use frequencies as low as possible, but within the specified range. JIS Z 3060 [13] stipulates the allowed probe frequency be determined based on the sound path distance with longer sound paths having lower frequen- cies. JIS Z 3060 allows 3.5–5 MHz probes be used on sound paths that are 100 mm (3.9″) or less. For second leg scans, this limit would be exceeded for a thickness of 1.4″ at a 45° incidence angle and at a thickness of 0.7″ at a 70° incidence angle. Anything over 250 mm (9.8″) is only allowed to be inspected using 2 MHz. 2.2 Research Methodology Four major research efforts constitute the approach taken to attain the objectives of the current research. The first was the evaluation of the critical flaw size for CJP bridge welds based on fracture mechanics using FFS methodology. Once the critical flaw size was determined, an experimental round robin testing program was then conducted using weld flaw specimens to compare test results using PAUT in accordance with AWS D1.5 Annex K to conventional UT, TOFD, and RT and to aid in the development of improvements to Annex K. The third step involved experimental testing that evaluated the acoustic properties of bridge weld and base metals and the development of calibration requirements. The fourth and final effort involved the use of computer modeling of ultra- sonic testing along with experimental ultrasonic testing of weld specimens in developing recommendations for revised scanning requirements and acceptance criteria in detecting and rejecting critical weld flaws. 2.2.1 Evaluation of Critical Flaw Size for Steel Bridge Welds An analytical parametric study was performed to establish the critical flaw size that would be considered rejectable for typical bridge CJP welds. The results were utilized in iden- tifying the critical flaw size that should be reliably detected and rejected and to establish revised acceptance and rejec- tion criteria. The critical flaw sizes were evaluated based on fracture mechanics using a BS 7910:2013 [2] FFS approach. These internal flaws are assumed to be cracks. The critical size of volumetric flaws was also evaluated through review of prior fatigue test results. This review highlighted that the fatigue crack growth threshold of volumetric flaws is similar to that of planar flaws. Therefore, FFS analysis can be applied for volumetric flaws by evaluating the maximum flaw size that will not undergo fatigue crack growth. FFS was performed to evaluate two different failure modes for planar flaws. The first is failure due to fatigue crack growth to ensure that internal defects do not grow in under cyclic loading. The second is failure due to brittle fracture. The analytical studies that were performed under this task included parametric studies of various plate geometries, welds, residual stress fields, flaw types, flaw sizes, and loca- tions. The results from the analytical program have identified the target critical flaw size. 2.2.2 Round Robin Experimental Testing Program A round robin testing program was performed in order to gain insight into the capabilities of the current technicians in the steel bridge industry and to identify best practices for improved flaw detection and flaw characterization. The round robin testing program was used to determine the mini- mum flaw size that could be reliably detected with enhanced ultrasonic methods and how the advanced methods compare with the historical conventional UT method. The round robin experimental testing program was performed by circulating weld flaw specimens among technicians in order to acquire inspection data from PAUT, conventional UT, TOFD, and RT. This data was used to compare the inspection results from

13 the various inspection methods. This comparison included determination of the hit/miss rate, rejection rate, frequency of false calls, accuracy of flaw height and length sizing, accu- racy of flaw type characterization, and technician variability. The results of the round robin testing program were used to improve development of future PAUT scanning proce- dures and acceptance criteria. These results highlighted that moving forward with the development of acceptance criteria based solely on the measurement of the flaw size is not feasible at present with the inaccuracy and unreliability in flaw size measurements using the current PAUT workforce. Therefore, the focus of the research was on improving the acceptance criteria based on maximum amplitude and flaw length in AWS D1.5 Annex K. An acceptance criteria based on physical measurements of the flaw height and length has also been provided in order to allow for alternative UT inspection methods or future technological improvements. 2.2.3 Development of Calibration Requirements for Variations in Acoustic Properties Experimental testing of various bridge welds and base materials has highlighted that the acoustic properties may vary considerably, including acoustic attenuation and shear wave velocity. Additional calibration requirements are neces- sary in order to account for possible differences between the calibration block and the test object. Not properly account- ing for these acoustic properties could result in large varia- tions of the amplitude of indications in the test object. The experimental results of the acoustic properties of various bridge base materials were used to generate bench- marked material models for ultrasonic inspection simu- lations using CIVA-UT. These simulations were used to develop requirements on the calibration block material and scanning parameters in order to limit possible error in ref- erence sensitivity. 2.2.4 Development of PAUT Scanning Procedures and Acceptance Criteria Simulations of PAUT inspections were performed using CIVA-UT to aid in the initial procedure development. The modeling incorporated weld flaws corresponding to the critical flaw sizes previously developed. These flaws serve as a “lower-bound” flaw set from which improved acceptance criteria were developed to consistently reject these flaws. As long as flaws of this size or larger are consistently rejectable, the procedure will be effective at removing critical flaws from service. Thus, the proposed acceptance criteria are grounded in fracture mechanics although they do not explicitly use flaw height measurement for evaluation. Rather, the future accep- tance criteria primarily use amplitude for flaw evaluation. The procedure was verified through experimental testing of weld flaw specimens to verify that the detection and rejection of critical weld flaws were improved.

Next: Chapter 3 - Findings and Application »
Acceptance Criteria of Complete Joint Penetration Steel Bridge Welds Evaluated Using Enhanced Ultrasonic Methods Get This Book
×
 Acceptance Criteria of Complete Joint Penetration Steel Bridge Welds Evaluated Using Enhanced Ultrasonic Methods
MyNAP members save 10% online.
Login or Register to save!
Download Free PDF

TRB’s National Cooperative Highway Research Program (NCHRP) Research Report 908: Acceptance Criteria of Complete Joint Penetration Steel Bridge Welds Evaluated Using Enhanced Ultrasonic Methods presents guidelines for evaluating complete joint penetration (CJP) welds in steel bridges and proposes modifications to the American Association of State Highway and Transportation Officials (AASHTO)/American Welding Society (AWS) D1.5.

Inspection of welds in steel bridges is necessary to ensure the quality of workmanship during the fabrication and construction process and later on when the bridge is in service. There are two non-destructive evaluation (NDE) methods for evaluation of complete joint penetration (CJP) welds in steel bridges: radiographic (RT) and ultrasonic (UT). Recent advances in enhanced ultrasonic methods, including the development of phased-array ultrasonic technology (PAUT), allow for efficient detection and characterization of flaws with the option of automated data collection and imaging.

Criteria for categorizing weld discontinuities as acceptable or unacceptable are codified in the AASHTO/AWS D1.5M/D1.5: Bridge Welding Code (BWC). However, these acceptance criteria do not reflect the full use of the capability of enhanced ultrasonic testing methods, and furthermore are not based on the effect of weld discontinuities on bridge performance (e.g., resistance to fatigue and fracture). In addition, some weld discontinuities that are not allowed according to BWC are potentially not harmful and may not decrease service life.

An updated acceptance criteria based on enhanced ultrasonic testing methods for evaluation of CJP welds in steel bridges was needed for fabricators and bridge owners.

READ FREE ONLINE

  1. ×

    Welcome to OpenBook!

    You're looking at OpenBook, NAP.edu's online reading room since 1999. Based on feedback from you, our users, we've made some improvements that make it easier than ever to read thousands of publications on our website.

    Do you want to take a quick tour of the OpenBook's features?

    No Thanks Take a Tour »
  2. ×

    Show this book's table of contents, where you can jump to any chapter by name.

    « Back Next »
  3. ×

    ...or use these buttons to go back to the previous chapter or skip to the next one.

    « Back Next »
  4. ×

    Jump up to the previous page or down to the next one. Also, you can type in a page number and press Enter to go directly to that page in the book.

    « Back Next »
  5. ×

    To search the entire text of this book, type in your search term here and press Enter.

    « Back Next »
  6. ×

    Share a link to this book page on your preferred social network or via email.

    « Back Next »
  7. ×

    View our suggested citation for this chapter.

    « Back Next »
  8. ×

    Ready to take your reading offline? Click here to buy this book in print or download it as a free PDF, if available.

    « Back Next »
Stay Connected!