US3787248A

US3787248A - Process for preparing aluminum alloys

Info

Publication number: US3787248A
Application number: US00291835A
Authority: US
Inventors: J Winter; W Setzer; H Cheskis
Original assignee: Individual
Current assignee: Individual
Priority date: 1972-09-25
Filing date: 1972-09-25
Publication date: 1974-01-22
Anticipated expiration: 1991-01-22
Also published as: IT996177B; SE433931B; SE397965B; JPS5615462B2; FR2200367B1; CA991062A; JPS5391884A; DE2342253A1; SE7703005L; JPS4970810A; JPS619180B2; DE2342253C2; FR2200367A1

Abstract

The present invention teaches a process for preparing high strength, improved formability aluminum base alloys suitable for use as can end stock, said high strength aluminum material of the present invention being readily compatible with aluminum can body material. The present invention also teaches an improved aluminum can having ends and body of substantially the same aluminum base alloy, which can as a whole is especially convenient to process in scrap reclamation procedures.

Description

Seller et al.

[ Man. 22, 1974 enoeess won PREPARING AIL r ALLOYS [76] Inventors: William C. Setzer, Hamden; llarvey l. Cheskis, Woodbridge; Joseph Winter, New Haven, all of Conn.

221 Filed: Sept. 25, 1972 21 Appl. No.: 291,835

[52] US. Cl l48/11.5 A [51] lint. Cl. C22f H04 [58] Field of Search 148/11.5 A

[56] References Cited UNITED STATES PATENTS 3,318,738 5/1967 Winter l48/l1.5 A 3,486,947 12/1969 Pryor et al. 148/11.5 A

Primary ExaminerW. W. Stallard Attorney, Agent, or FirmRobert H. Bachman [5 7] ABSTRACT The present invention teaches a process for preparing high strength, improved formability aluminum base alloys suitable for use as can end stock, said high strength aluminum material of the present invention being readily compatible with aluminum can body material. The present invention also teaches an improved aluminum can having ends and body of substantially the same aluminum base alloy, which can as a whole is especially convenient to process in scrap reclamation procedures.

12 Claims, 2 Drawing lFigures TENTH] JkN 22 I974 l PROCESS FOR PREPARING ALUMINUM ALLOYS BACKGROUND OF THE INVENTION It is well known that there has been a rapid growth in the use of aluminum cans, especially of the easy open variety. This rapid growth has resulted in a national effort to retrieve and recycle as many aluminum cans as possible, particularly among public spirited beverage companies and ecologicallyminded citizens.

One of the most significant difficulties with recycling most current easy open aluminum cans is the fact that different alloys are generally utilized for the can end and for the can body. For example, alloys 5082 or 5182 are commonly used for the can end and alloy 3004 is commonly used for the can body. Thus, in recycling these two-piece aluminum cans, one must contend with a mixed alloy scrap, which is inconvenient and difficult to process and in fact highly undesirable.

The can end alloys with their relatively high magnesium content, for example, alloys 5082 and 5182, are a major cause of recycling problems. In remelting the cans, the magnesium oxidizes readily and is lost. In addition, the oxides can be trapped in the melt and result in inferior ingots. On the other hand, the can body alloys, for example, alloy 3004, with a lower magnesium content, have not been successfully used for can ends because of low strength and ductility properties. The

severe forming requirements necessary to produce a satisfactory can end have not been met by alloy 3004.

Accordinglyfit is a principal object of the present invention to provide a process for preparing high strength aluminum alloys having improved formability suitable for use as can end stock.

It is a further object of the present invention to provide a process as aforesaid which enables the production of aluminum can ends having substantially the same composition as the aluminum can body.

It is a further object of the present invention to provide an improved aluminum can wherein the ends and body thereof have substantially the same composition.

SUMMARY OF THE INVENTION In accordance with the present invention, it has now been found that the foregoing objects and advantages may be readily obtained. The process of the present invention provides a high strength aluminum base alloy having improved formability and comprises:

1 A. providing an aluminum base alloy consisting essentially of from 0.5 2.0 percent manganese, from 0.4 2.0 percent magnesium, balance essentially aluminum;

B. homogenizing said alloy at a temperature of from 850F to l,l50F for from 2 hours to 24 hours;

C. rolling said alloy with a starting temperature in the range 650- 950F, with a total reduction in excess of 20 percent to a gage of 0.5 inch or above;

D. further rolling said alloy with a starting temperav t ure in the range 400800F, with a total reduction in excess of 20 percent, preferably from 45 to 85 percent to a gage of 0. 100 inch or above; E. further rolling said alloy at a starting temperature less than 400F,prefe rably cold rolling, with a to tal- 2-2 thereof.

reduction in excess of 20 percent, preferably 40 80 percent; and 7 F. holding said alloy at a temperature between 200 4 KBE IQd 2 timeiat s s fivss but no greater than defined in the following formula: T (12 log t) 12,500, wherein T is the temperature in degrees Kelvin and I is the maximum time in minutes at temperature T. It is preferred to repeat steps E. and F., optimally a plural ity of times.

In the preferred embodiment, the alloy is thermally stabilized at a temperature of from 250 to 450F for a period of time of at least 5 seconds but no greater than defined by the formula set forth above, wherein T and t are as defined above. The stabilization treatment may be combined with the standard coating operation in which the can end stock is coated with a polymeric material prior to use.

The present invention also resides in an improved aluminum can having ends and body thereof of substantially the same composition, namely, both the ends and body thereof consist essentially of from 0.4 2.0 percent magnesium, 0.5 2.0 percent manganese, balance essentially aluminum, wherein at least one end thereof has a minimum stretch forming height to diameter ratio of 0.210 and generally 0.242.

BRIEF ESQRWTIQ LQ BYY EQSW FIG. 1 illustrates a fragmentary perspective view of a sealed container of the present invention; and

FIG. 2 is a sectional view on an exaggerated scale of the tab element illustrated in FIG. 1 taken through line DETAILED DESCRIPTION As indicated hereinabove, the process of the present invention enables the preparation of an improved aluminum can wherein the ends and body thereof have substantially the same chemical composition, as indicated hereinabove.

It is a further and surprising advantage of the process of the present invention that this process imparts significant improved physical characteristics to the can top material of the present invention. Hence, the aluminum material processing herein is characterized by suprisingly improved strength, ductility, formability and thermal stability. The improved characteristics of the can top of the present invention enable this material to be readily processed into commercial can ends utilizing conventional manufacturing equipment. This is a particular advantage in view of the large scale use of this equipment. Furthermore, the improved physical characteristics of the alloy herein, imparted by the process surprising advantage of the present invention. These characteristics will be discussed in greater detail hereinbelow.

As an example of the foregoing, conventional materials used currently for can ends include aluminum alloy 5182 having the following composition limits: Silicon, up to 0.20 percent; iron, up to 0.35 percent; copper, up to 0.15 percent; manganese, from 0.20 to 0.50 percent; magnesium, from 4.0 to 5.0 percent; chromium, up to 0.10 percent; zinc, up to 0.25 percent; titanium, up to 0.10 percent; balance aluminum. The process of the present invention provides the following features on the alloys processed herein, which have substantially the same composition as the aluminum can body currently used. In particular reference to aluminum alloy 3004, which has the following composition limits: Manganese, from 1.0 to 1.5 percent; magnesium, from 0.8 to 1.3 percent; zinc, up to 0.25 percent; balance aluminum, the following represents advantages of the processing of the present invention. The processing of the present invention achieves superior stretch forming characteristics over the conventionally used alloy 5182. Furthermore, in the final can end configuration, the 3004 can end processed in accordance with the present invention requires less load than conventional 5182 to initiate tab removal and yet still maintain safe handling characteristics in the resultant can end. This represents a particularly desirable feature since the can may be safely handled during filling, packing and shipping, and still be more easily opened by the ultimate consumer. A particular advantage of the material processed in accordance with the present invention is its superior strength, ductility combination over the same material processed in a conventional manner. Hence, the process of the present invention permits an alloy, such as 3004, to be readily formed into can ends because of the enhanced ductility imparted thereby, and yet material mateiral is still strong enough to safely contain the pressurized contents.

An additional advantage of the material processed in accordance with the present invention is that it achieves superior thermal stability to conventionally processed materials such that a high yield strength can be maintained after the final thermal treatment. Furthermore, this enhanced thermal stability permits a broader range of thermal treatment during the coating process over conventionally processed material, that is, higher temperatures for longer times may be utilized which represents an advantage commercially.

An additional and surprising advantage of the process ofthe present invention is that it enables a can end material which is more corrosion resistant then can ends formed from conventional materials such as aluminum alloy 5182. Also, no galvanic corrosion is possible since the entire can utilizes one alloy throughout.

As indicated hereinabove, the process of the present invention provides an aluminum base alloy consisting of from 0.5 to 2.0 percent manganese, from 0.4 to 2.0 percent magnesium, balance essentially aluminum. The alloy of the present invention preferably contemplates the inclusion of the following optional constituents, all fiwhisbmayheptcsent. n m unt as 19w as -9 and preferably as low as 0.0 l percent:Silicon, up to 0.5 percent; iron, up to 1 percent; copper, up to 0.5 percent; zinc, up to 0.5 percent; chromium, up to 0.2 per- Cent; ium 2.9.99. ,.ns snttlz tetu e 299} percent; and titanium, up to 0.2 percent. In addition to the foregoing, other components may be present in an amount of each 0.05 percent, total up to 0.20 percent. Naturally, conventional impurities may be contemplated.

In accordance with the present invention, the aluminum alloys utilized herein may be cast in any desired manner. The particular method of casting is not critical and any commercial method may be conveniently employed, such as direct chill or tilt mold casting. It is preferred to utilize direct chill casting to provide a finely dispersed uniform particle size of second phase constituents. After casting, a homogenization or solutionization treatment is utilized for a sufficient period of time to avoid macro-segregation. This homogenization treatment should be performed at a temperature from 850F to 1 150F and preferably from 1,000F to 1,l25F and the ingot should be held at temperature for from 2 hours to 24 hours.

The process of the present invention contemplates a series of rolling steps, each of which falls within critical temperature limits. The first rolling step of the present invention is with a starting temperature in the range of 650 to 950F, with the total reduction in excess of 20 percent. Naturally, the total reduction is dependent upon ingot gage, with the material being rolled in this step to a gage of 0.5 inch or above. This rolling step is intended to break up the cast structure and get the material to a workable gage.

The material is then further rolled with a starting temperature in the range of 400 to 800F and with a total reduction in excess of 20 percent. The total reduction in this step is preferably from 45 to 85 percent and optimally from 50 to percent. The material is rolled in this step to gage of 0.100 inch or above and preferably to a gage of 0.175 to 0.250 inch. This rolling step is particularly critical in that it has been found that the starting temperature must be kept within the foregoing range in order to insure adequate strength prior to cold rolling.

The material is then further rolled at a starting temperature less than 400F, and preferably cold rolled, with a total reduction in this step in excess of 20 percent and preferably from 40 to percent. The gage requirements here are dictated by the amount of reduction employed and the final gage requirements, e.g., the final can end stock gage.

The material is then held at a temperature between 250 and 450F for at least five seconds, but for a period of time no greater than defined in the following formula: T 12 log t) 12,500, wherein T is the temperature in degrees Kelvin and t is the maximum time at temperature T. The temperature time combination should be such that the tensile properties of the metal are reduced no more than 20 percent. It is preferred to utilize a holding time of from 30 minutes to 8 hours and a temperature range of from 250 to 350F.

In accordance with the process of the present invention, the cold rolling and holding steps thereof should preferably be repeated, optimally a plurality of times. Generally, no more than two or three additional cycles are utilized.

7 As indicated hereinabove, it has been found that the foregoing process imparts to the alloys herein improved strength, ductility, formability and thermal stability so that they can be readilymufagu dinto easy open can ends on a commerical basis in a simple, convenient and expeditious manner.

The process of the present invention preferably contemplates a final thermal stabilizing step. This thermal stabilizing step may be readily achieved as an inherent feature of the coating process to which these materials are conventionally subjected. Conventionally, the coating process comprises coating the can material with a polymeric material, such as an epoxy, polyvinyl chloride or a polyolefin. This step is intended to avoid deleterious reaction between the contents of the can and the aluminum alloy can or can top material. Normally, the coating and curing process involves a certain holding and elevated temperature combination. Thus, the thermal stabilizing step of the present invention contemplates holding said material at a temperature of from 250 to 450F for a period of time of at least 5 seconds but no greater than that which is defined by the formula set forth above. Preferably, the holding time is from 4 hours to 24 hours and the preferred temperature is from 250 to 375F. Naturally, the optimal holding times and temperatures are interrelated. The stabilizing treatment is intended to insure uniform properties throughout the coil and' is important in maintaining these uniform properties. In this step the yield strength properties should not drop more than 50 percent.

Thus; the present invention provides an improved sheet metal product, an improved can end and also an improved aluminum can. As indicated hereinabove, it is a particular advantage of the present invention that substantially the same alloy can be utilized for the can ends and body. The composition consists essentially of from 0.4 to 2.0 percent magnesium, 0.5 to 2.0 percent manganese and the balance essentially aluminum. Naturally, additives and impurities may be utilized, so that the following limits are contemplated: Silicon, up to 0.5

percent; iron, up to 1.0 percent; copper, up to 0.5 percent; chromium, up to 0.2 percent; zinc, up to 0.5 percent; titanium, up to 0.2 percent; others up to 0.05 percent each, total 0.20 percent. Naturally, the present invention contemplates variations within the foregoing limits so that identical alloys need not necessarily be utilized for the can ends and body.

It is a particular advantage of the present invention that it enables the use of relatively low magnesium alloys for can end stock, such as alloy 3004. Furthermore, the sheet metal product of the present invention has sufficient formability to be processed into a can end, with a minimum stretch forming height to diameter ratio of 0.242. The sheet metal product of the present invention possesses a minimum yield strength of 42,000 psi at 0.2 percent offset and a minimum tensile elongation of 3 percent for a gage of 0.020 inch. Furthermore, the strip can be thermally treated, for example, at 350F for 13 hours and still maintain a minimum yield strength of 42,000 psi. The foregoing represents highly advantageous and surprisingadvantages.

Turning more specifically to the drawings which form a part of the present specification, as is shown in FIGS. 1 and 2 thereof, a container 1 has a body portion 2 and an end wall 3. The end wall 3 is provided with a removable portion or tear strip 4 which is defined by scored line or lines 5. Within the tear strip 4 at one end thereof is affixed a pull tab or ring pull 6 which is secured to the tear strip 4 by conventional integral rivet 7. The can end 3 is secured to the body portion 2 by means of fold lock seam 8.

In operation, the can end is opened by pulling on pull tab or ring pull 6 which tears along scored lines 5, thus removing the tear strip 4 away from the can end.

As is shown, the ring pull or pull tab is secured to the tear strip by means of an integral rivet which is formed directly from the container end. The fabrication of the integral rivet requires that the can end material be suf ficiently formable to be made into a configuration to hold the ring attachment to the can end without fracturing in handling. The integral rivet is formed in a plurality of operations which require a combination of good strength and ductility, as has been pointed out hereinabove. A typical method for forming the integral rivet may be briefly summarized below.

Step 1 is a stretch forming operation in which a hemispherical bubble is produced vertically downward. The purpose of the formation of this hemispherical bubble is to thin the metal in the central portion of the can end and thus provide extra metal for forming. In addition, this reduces the severity of the Step 2 forming operation.

Step2. In this step a small protrusion is produced vertically upward by forcing the Step I bubble in a reverse direction into a smaller die opening. Thus, the operation in Step 2 is a combination of bending, stretch forming and drawing.

Step 3. This is the final step. After the Step 2 protrusion is formed, the can end is scored to form the tab or tear strip portion and several minor protrusions are formed to add buckling stability to the can end when the tab or tear strip is opened by the consumer. In'this final step, the ring pull is placed around the Step 2 protrusion which is then upset to form the final integral rivet configuration.

As an example, a can end was made in accordance with the foregoing steps. The Step I bubble was 0.080 inch in depth and the finished inside diameter was 0.394 inch. Thus, the height to diameter ratio in this Step 1 was 0.203. The maximum metal thinning inthis Step 1 was from 0.0128 to 0.00975 inch, or a reduction of 23.2 percent. In the Step 2 operation, the final protrusion height was 0.066 inch with an inside diameter of 0.0968 inch. The total height to diameter ratio for Step 2 was 0.685. After the Step 3 operation, the top portion of the rivet was severely thinned in compression approximately 50 percent from 0.008 to 0.004 inch.

Thus, it can be seen that the sheet metal article of the present invention must have a high degree of strength, ductility and formability in order to be processed to the can top material of the present invention.

In the formation of can top material from the sheet metal of the present invention, the coil of processed metal is first subjected to a standard coating operation in which the can end stock is coated with a polymeric material prior to use, such as an epoxy base resin. The metal may pass through a continuous line where it is first covered with a solvent resin coating. It then passes through a furnace where the solvent is baked out leaving the resin coating. Metal temperature during the bake cycle is conventionally in excess of 300F for a time period of from I to 3 minutes. The coated metal is then fabricated into easy open can ends by stamping circular blanks from the coil, forming an end flange to provide a locus for attachment to the can body and providing a coating of latex to the flange area for use as a sealant. The curled blanks are then processed as indicated hereinabove to attach the pull tab or ring pull to the can top through the integral rivet. The top with pull tab attachment is then affixed to the can body by means of the curled flange, with the latex acting as a pressure sealant for the system.

The process and article of the present invention will be more readily understandable from a consideration of the following illustrative examples.

EXAMPLE 1 Aluminum alloy 3004 was provided having the composition set forth in Table l below.

The material was processed in the following manner. The material was homogenized at lO75F for 12 hours followed by hot rolling at a starting temperature of 800F using 10 percent reductions per pass from 2.00 to 0.600 inch. with a reheat after each reduction at 800F for 5 minutes. The material was then warm rolled at a starting temperature of 550F using percent reductions per rolling pass from 0.600 to 0.250 inches, with a reheat after each pass at 550F for 5 minutes. The material was then cold rolled from 0.25 to 0.060 inch using 10 percent reductions per pass. The metal was then heat treated for 2 hours at 260F followed by cold rolling with a 10 percent reduction per pass from a gage of 0.060 to 0.030 inch. The material was then heat treated at 260F for 2 hours followed by cold rolling to final gage. The material was then stabilized at 350F for 1 hour. The foregoing represents the processing of the present invention.

EXAMPLE ll The material set forth in Table l above was processed for comparative purposes in the following manner. The material was homogenized at a temperature l050F for 12 hours followed by hot rolling to 0.250 inch gage using a starting temperature of 825F and a finish temperature of 650F. The material was then cold rolled from 0.250 inch to final gage. The material was stabilized at 350F for 1 hour.

EXAMPLE III In accordance with this Example, alloy 5182 was processed in the manner set forth below. The alloy had the composition set forth in Table ll below.

TABLE ll Composition Silicon 0.138 71 Iron 0.2 l71 Manganese 0.34%

Magnesium 4.50%

Chromium 0.5971

Titanium 0.096%

Aluminum Essentially Balance The material was homogenized at a 975F for 15 hours followed by hot rolling at 825F to 0.150 inch using a 10 percent reduction per pass and reheating at 825F for 5 minutes after each pass. The material was then cold rolled from 0.150 to 0.0125 inch and then stablized at 450F for 15 minutes.

EXAMPLE IV The material of the present invention processed in accordance with Example I above has improved yield strength to ductility properties when compared to the conventionally processed material of Example ll above. The strength to ductility ratio is important in producing a can end since the product must have sufficient strength and be sufficiently ductile to be formed into the integral rivet as set forth hereinabove. In order to determine these properties, standard 2 inches gage length tensile tests were performed on samples of material processed in accordance with Example l and Example ll, with the exception that the material of Example ll was not given a final stabilizing treatment since this would degrade the strength properties. Comparison is made at the same metal thickness and the same yield strength, ductility was measured in terms of percent elongation in a standard tensile test, with the test being performed at room temperature at a cross-head speed of 0.050 inch per minute. The increase in tensile elongation for the material processed in accordance with the present invention over the conventionally processed material is significant. The results are shown in Table 11] below.

This example illustrates the improved stretch forming characteristics of the material processed in accordance with Example I over the material processed in Example lll. Samples processed in accordance with Examples 1 and Ill were tested for stretch formability, a property which is critical in the formation of the integral rivet. This test was conducted by penetrating the metal with a punch of 0.100 inch diameter until the metal failed. The depth of penetration (H) at failure divided by the punch diameter (D) is a measure of the stretch forming capability of the metal. The following table shows the stretch forming capability (H/D) of the two materials. It can be clearly seen that the material processed in accordance with the present invention has improved stretch forming characteristics.

This example illustrates that the material processed in accordance with the present invention has enhanced TABLE VI Material Time at 350F to Reach 42,000 psi Yield Strength EXAMPLE l 13 Hours EXAMPLE ll 32 Minutes This invention may be embodied in other forms or carried out in other ways without departing from the spirit or essential characteristics thereof. The present embodiment is therefore to be considered as in all respects illustrative and not restrictive, the scope of the invention being indicated by the appended claims, and all changes which come within the meaning and range of equivalency are intended to be embraced therein.

What is claimed is:

l. A process for providing high strength and improved formability in an aluminum base alloy which comprises:

A. providing an aluminum base alloy consisting essentially of from 0.5 to 2.0 percent manganese, from 0.4 to 2.0 percent magnesium, balance essentially aluminum;

C. rolling said alloy at a starting temperature in the range of 650 to 950F, with a total reduction in excess of percent, to a gage of 0.5 inch or above;

D. further rolling said alloy at a starting temperature in the range of 400 to 800F, with a total reduction in excess of 20 percent;

E. further rolling said alloy at a starting temperature of less than 400F, with a total reduction in excess of 20. percent; and

F. holding said alloy at a temperature between 200 and 450F for a period of time of at least 5 seconds but no greater than defined in the following formula: T l2 log t) 12,500, where T is the temperature in degrees Kelvin and t is the maximum time in minutes at temperature T.

2. A process according to claim 1 wherein steps (E) and (F) are repeated.

3. A process according to claim 2 wherein the material is held in step (F) for a period of time of from 30 minutes to 8 hours.

4. A process according to claim 1 wherein the material is thermally stabilized following step (F) at a temperature of from 250 to 450F for a period of time defined by the following formula: T 12 log t) 12,500, wherein T and t are as defined above.

5. A process according to claim 4 wherein following step (F) the material is coated with a polymeric material at an elevated temperature.

6. A process according to claim 5 wherein the material is thermally stabilized during the coating operation.

7. A process according to claim 4 wherein the material is thermally stabilized at a period of time of from 4 hours to 24 hours.

8. A process according to claim 2 wherein the mate rial is rolled in step (D) with a total reduction of from 45 to 85 percent to a gage of 0.100 inch or above.

9. A process according to claim 2 wherein the material is cold rolled in step (E) with a total reduction of from 40 to percent.

10. A process according to claim 2 wherein said alloy is aluminum alloy 3004.

11. A process according to claim 2 wherein said alloy contains: Silicon, up to 0.5 percent; iron, up to l percent; copper, up to 0.5 percent; zinc, up to 0.5 percent; chromium, up to 0.2 percent; beryllium, up to 0.01 percent; boron, up to 0.01 percent; titanium, up to 0.2 percent; others each up to 0.05 percent, total up to 0.20 percent.

12. A process according to claim 2 wherein steps (E) and (F) are repeated a plurality of times.

Claims

2. A process according to claim 1 wherein steps (E) and (F) are repeated.
3. A process according to claim 2 wherein the material is held in step (F) for a period of time of from 30 minutes to 8 hours.
4. A process according to claim 1 wherein the material is thermally stabilized following step (F) at a temperature of from 250* to 450*F for a period of time defined by the following formula: T (12 + log t) 12,500, wherein T and t are as defined above.
5. A process according to claim 4 wherein following step (F) the material is coated with a polymeric material at an elevated temperature.
6. A process according to claim 5 wherein the material is thermally stabilized during the coating operation.
7. A process according to claim 4 wherein the material is thermally stabilized at a period of time of from 4 hours to 24 hours.
8. A process according to claim 2 wherein the material is rolled in step (D) with a total reduction of from 45 to 85 percent to a gage of 0.100 inch or above.
9. A process according to claim 2 wherein the material is cold rolled in step (E) with a total reduction of from 40 to 80 percent.
10. A process according to claim 2 wherein said alloy is aluminum alloy 3004.
11. A process according to claim 2 wherein said alloy contains: Silicon, up to 0.5 percent; iron, up to 1 percent; copper, up to 0.5 percent; zinc, up to 0.5 percent; chromium, up to 0.2 percent; beryllium, up to 0.01 percent; boron, up to 0.01 percent; titanium, up to 0.2 percent; others each up to 0.05 percent, total up to 0.20 percent.
12. A process according to claim 2 wherein steps (E) and (F) are repeated a plurality of times.